Initial reading of data
Miriam Lachs
2024-12-06
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(gtsummary)
library(emulator)## Loading required package: mvtnormtest_df=read_csv('Project_1_data.csv') %>% janitor::clean_names() ## Rows: 948 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (10): Gender, EthnicGroup, ParentEduc, LunchType, TestPrep, ParentMarita...
## dbl (4): NrSiblings, MathScore, ReadingScore, WritingScore
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.test_df=test_df %>%
mutate(is_first_child=case_when(
is.na(is_first_child) &nr_siblings==0 ~ 'yes',
TRUE ~is_first_child
)) %>%
mutate(gender=as.factor(gender),
ethnic_group=as.factor(ethnic_group),
parent_educ=as.factor(parent_educ),
lunch_type=as.factor(lunch_type),
test_prep=as.factor(test_prep),
parent_marital_status=as.factor(parent_marital_status),
practice_sport=as.factor(practice_sport),
is_first_child=as.factor(is_first_child),
transport_means=as.factor(transport_means),
wkly_study_hours=as.factor(wkly_study_hours)) %>% drop_na()summary(test_df)## gender ethnic_group parent_educ lunch_type
## female:315 group A: 50 associate's degree:129 free/reduced:207
## male :275 group B:123 bachelor's degree : 71 standard :383
## group C:175 high school :123
## group D:156 master's degree : 39
## group E: 86 some college :116
## some high school :112
## test_prep parent_marital_status practice_sport is_first_child
## completed:210 divorced: 93 never : 69 no :192
## none :380 married :344 regularly:219 yes:398
## single :138 sometimes:302
## widowed : 15
##
##
## nr_siblings transport_means wkly_study_hours math_score
## Min. :0.000 private :229 < 5 :156 Min. : 0.00
## 1st Qu.:1.000 school_bus:361 > 10 :104 1st Qu.: 56.25
## Median :2.000 10-May:330 Median : 67.00
## Mean :2.129 Mean : 66.74
## 3rd Qu.:3.000 3rd Qu.: 78.00
## Max. :7.000 Max. :100.00
## reading_score writing_score
## Min. : 17.00 Min. : 10.00
## 1st Qu.: 60.00 1st Qu.: 58.00
## Median : 70.00 Median : 69.00
## Mean : 69.87 Mean : 68.92
## 3rd Qu.: 81.00 3rd Qu.: 79.00
## Max. :100.00 Max. :100.00test_df %>%
ggplot(aes(x=math_score))+geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
test_df %>%
ggplot(aes(x=reading_score))+geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
test_df %>%
ggplot(aes(x=writing_score))+geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
stu_data=table(test_df$gender,test_df$ethnic_group)
chisq.test(stu_data)##
## Pearson's Chi-squared test
##
## data: stu_data
## X-squared = 7.211, df = 4, p-value = 0.1251# Loop through pairs of columns and run the chi-square test
for (i in 1:(11 - 1)) {
for (j in (i + 1):11) {
# Get the two columns to test
col1 <- test_df[[i]]
col2 <- test_df[[j]]
contingency_table <- table(col1, col2)
# Perform the chi-square test
chi_test <- chisq.test(contingency_table)
#PRint the results
if(chi_test$p.value<.05){
cat("Chi-square test for columns", colnames(test_df)[i], "and", colnames(test_df)[j], "\n")
print(chi_test)
}
}
}## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect## Chi-square test for columns gender and nr_siblings
##
## Pearson's Chi-squared test
##
## data: contingency_table
## X-squared = 15.086, df = 7, p-value = 0.03491## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect## Chi-square test for columns is_first_child and nr_siblings
##
## Pearson's Chi-squared test
##
## data: contingency_table
## X-squared = 45.266, df = 7, p-value = 1.214e-07## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrect
## Warning in chisq.test(contingency_table): Chi-squared approximation may be
## incorrectggplot(test_df, aes(x = nr_siblings, fill = gender)) +
geom_bar(position = "fill") +
labs(y = "Proportion", title = "Pairwise Relationship")
ggplot(test_df, aes(x = nr_siblings, fill = is_first_child)) +
geom_bar(position = "fill") +
labs(y = "Proportion", title = "Pairwise Relationship")
Writing Score
df_4_mdl_write=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score)
full_fit_write=lm(writing_score ~ .^2,data=df_4_mdl_write)summary(full_fit_write)##
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36.097 -6.757 0.000 7.512 25.909
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 77.5056 16.5568
## gendermale -11.5459 8.4352
## ethnic_groupgroup B -14.6713 14.2358
## ethnic_groupgroup C -23.6506 13.4300
## ethnic_groupgroup D -6.5467 14.6194
## ethnic_groupgroup E -0.6452 13.7011
## parent_educbachelor's degree 32.2994 14.9679
## parent_educhigh school 8.9108 12.3906
## parent_educmaster's degree -13.3428 20.4548
## parent_educsome college -9.2192 12.1578
## parent_educsome high school 0.3856 11.7932
## lunch_typestandard 3.1104 8.3745
## test_prepnone -18.8143 8.7378
## parent_marital_statusmarried 16.0430 11.1254
## parent_marital_statussingle 10.7223 13.3899
## parent_marital_statuswidowed 43.4838 39.5573
## practice_sportregularly -23.0508 13.3196
## practice_sportsometimes -19.7741 13.2523
## is_first_childyes 14.2090 9.5945
## transport_meansschool_bus -3.2352 8.4932
## wkly_study_hours> 10 -19.5441 13.0836
## wkly_study_hours10-May 1.6614 10.5143
## gendermale:ethnic_groupgroup B 4.3932 5.3431
## gendermale:ethnic_groupgroup C 9.3149 5.1384
## gendermale:ethnic_groupgroup D 5.8109 5.1043
## gendermale:ethnic_groupgroup E 5.3001 5.6595
## gendermale:parent_educbachelor's degree -3.1793 4.4945
## gendermale:parent_educhigh school 1.0620 3.6653
## gendermale:parent_educmaster's degree 9.9155 6.2928
## gendermale:parent_educsome college -4.1300 3.8491
## gendermale:parent_educsome high school 0.2529 3.7808
## gendermale:lunch_typestandard -1.2039 2.6255
## gendermale:test_prepnone -0.2240 2.6166
## gendermale:parent_marital_statusmarried -0.4821 3.7301
## gendermale:parent_marital_statussingle -0.1518 4.2288
## gendermale:parent_marital_statuswidowed 1.2933 18.3113
## gendermale:practice_sportregularly -3.0622 4.4464
## gendermale:practice_sportsometimes -3.2602 4.4697
## gendermale:is_first_childyes 3.0435 2.7466
## gendermale:transport_meansschool_bus -0.1546 2.5389
## gendermale:wkly_study_hours> 10 -3.8677 3.9831
## gendermale:wkly_study_hours10-May -2.6013 3.0208
## ethnic_groupgroup B:parent_educbachelor's degree -8.3345 12.4645
## ethnic_groupgroup C:parent_educbachelor's degree -8.4712 12.4445
## ethnic_groupgroup D:parent_educbachelor's degree -9.6856 12.3505
## ethnic_groupgroup E:parent_educbachelor's degree -16.9547 14.0557
## ethnic_groupgroup B:parent_educhigh school -16.1825 7.8036
## ethnic_groupgroup C:parent_educhigh school -10.7952 7.5005
## ethnic_groupgroup D:parent_educhigh school -7.6467 7.6256
## ethnic_groupgroup E:parent_educhigh school -11.4328 8.4924
## ethnic_groupgroup B:parent_educmaster's degree 4.9001 14.9754
## ethnic_groupgroup C:parent_educmaster's degree -7.4679 13.9097
## ethnic_groupgroup D:parent_educmaster's degree 2.9024 14.1310
## ethnic_groupgroup E:parent_educmaster's degree 1.3629 14.8684
## ethnic_groupgroup B:parent_educsome college 3.2143 8.6301
## ethnic_groupgroup C:parent_educsome college 5.9797 8.1460
## ethnic_groupgroup D:parent_educsome college 9.5674 8.4844
## ethnic_groupgroup E:parent_educsome college 2.6023 8.5774
## ethnic_groupgroup B:parent_educsome high school -17.7650 8.2716
## ethnic_groupgroup C:parent_educsome high school -10.3880 7.7610
## ethnic_groupgroup D:parent_educsome high school -6.6709 7.8120
## ethnic_groupgroup E:parent_educsome high school -4.3383 8.3877
## ethnic_groupgroup B:lunch_typestandard 3.1284 5.5561
## ethnic_groupgroup C:lunch_typestandard 6.9223 5.3886
## ethnic_groupgroup D:lunch_typestandard 3.8322 5.3042
## ethnic_groupgroup E:lunch_typestandard -0.1953 6.1469
## ethnic_groupgroup B:test_prepnone 2.4242 5.6685
## ethnic_groupgroup C:test_prepnone 6.4991 5.3175
## ethnic_groupgroup D:test_prepnone 4.2882 5.3281
## ethnic_groupgroup E:test_prepnone 10.4184 5.7998
## ethnic_groupgroup B:parent_marital_statusmarried 4.0514 7.6528
## ethnic_groupgroup C:parent_marital_statusmarried -0.2301 7.0469
## ethnic_groupgroup D:parent_marital_statusmarried -10.9053 6.9504
## ethnic_groupgroup E:parent_marital_statusmarried -4.3960 7.6897
## ethnic_groupgroup B:parent_marital_statussingle 10.5415 9.0607
## ethnic_groupgroup C:parent_marital_statussingle 2.1275 8.5665
## ethnic_groupgroup D:parent_marital_statussingle -2.6676 8.2778
## ethnic_groupgroup E:parent_marital_statussingle 3.1117 9.5410
## ethnic_groupgroup B:parent_marital_statuswidowed 73.8433 101.3778
## ethnic_groupgroup C:parent_marital_statuswidowed 114.3340 82.3923
## ethnic_groupgroup D:parent_marital_statuswidowed 12.1039 83.0580
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 14.5020 10.1514
## ethnic_groupgroup C:practice_sportregularly 15.9609 10.0599
## ethnic_groupgroup D:practice_sportregularly 11.8248 11.2295
## ethnic_groupgroup E:practice_sportregularly 12.9574 10.2802
## ethnic_groupgroup B:practice_sportsometimes 12.6309 10.8289
## ethnic_groupgroup C:practice_sportsometimes 22.0758 10.5328
## ethnic_groupgroup D:practice_sportsometimes 12.1147 11.6115
## ethnic_groupgroup E:practice_sportsometimes 12.5339 10.5863
## ethnic_groupgroup B:is_first_childyes 9.7409 5.6253
## ethnic_groupgroup C:is_first_childyes 3.4474 5.3065
## ethnic_groupgroup D:is_first_childyes 1.8617 5.3681
## ethnic_groupgroup E:is_first_childyes 2.7052 6.0462
## ethnic_groupgroup B:transport_meansschool_bus -7.4751 5.6284
## ethnic_groupgroup C:transport_meansschool_bus -11.2746 5.1972
## ethnic_groupgroup D:transport_meansschool_bus -5.1875 5.1920
## ethnic_groupgroup E:transport_meansschool_bus -12.0724 6.1289
## ethnic_groupgroup B:wkly_study_hours> 10 -5.9602 9.5818
## ethnic_groupgroup C:wkly_study_hours> 10 1.9360 9.4624
## ethnic_groupgroup D:wkly_study_hours> 10 6.7581 9.4492
## ethnic_groupgroup E:wkly_study_hours> 10 0.4986 10.2937
## ethnic_groupgroup B:wkly_study_hours10-May -5.8066 8.0474
## ethnic_groupgroup C:wkly_study_hours10-May 1.8457 7.8744
## ethnic_groupgroup D:wkly_study_hours10-May 2.9555 8.0075
## ethnic_groupgroup E:wkly_study_hours10-May -1.4251 8.6215
## parent_educbachelor's degree:lunch_typestandard 0.9925 4.8362
## parent_educhigh school:lunch_typestandard 0.9740 3.9027
## parent_educmaster's degree:lunch_typestandard 6.9772 7.1530
## parent_educsome college:lunch_typestandard 5.3543 3.9343
## parent_educsome high school:lunch_typestandard 5.7895 4.0754
## parent_educbachelor's degree:test_prepnone -1.3131 4.4623
## parent_educhigh school:test_prepnone 1.8447 4.2737
## parent_educmaster's degree:test_prepnone -2.3089 7.6077
## parent_educsome college:test_prepnone -1.8819 4.0056
## parent_educsome high school:test_prepnone 2.4708 3.8740
## parent_educbachelor's degree:parent_marital_statusmarried -17.2754 7.9642
## parent_educhigh school:parent_marital_statusmarried 2.5731 5.6012
## parent_educmaster's degree:parent_marital_statusmarried 4.5317 8.1036
## parent_educsome college:parent_marital_statusmarried -4.8368 5.5157
## parent_educsome high school:parent_marital_statusmarried -3.8229 5.4356
## parent_educbachelor's degree:parent_marital_statussingle -16.6290 8.5852
## parent_educhigh school:parent_marital_statussingle 6.4988 6.1186
## parent_educmaster's degree:parent_marital_statussingle 1.5045 8.6504
## parent_educsome college:parent_marital_statussingle -4.6580 6.1430
## parent_educsome high school:parent_marital_statussingle -3.7573 6.0684
## parent_educbachelor's degree:parent_marital_statuswidowed -20.6113 84.4043
## parent_educhigh school:parent_marital_statuswidowed -74.8517 92.8678
## parent_educmaster's degree:parent_marital_statuswidowed -98.2733 48.6482
## parent_educsome college:parent_marital_statuswidowed -87.5058 60.9959
## parent_educsome high school:parent_marital_statuswidowed -61.8441 73.1065
## parent_educbachelor's degree:practice_sportregularly 1.8608 8.2226
## parent_educhigh school:practice_sportregularly -10.9775 7.0762
## parent_educmaster's degree:practice_sportregularly 1.5289 9.9993
## parent_educsome college:practice_sportregularly -0.1518 7.1960
## parent_educsome high school:practice_sportregularly -3.2753 6.9492
## parent_educbachelor's degree:practice_sportsometimes -8.3616 7.8902
## parent_educhigh school:practice_sportsometimes -10.1532 6.7020
## parent_educmaster's degree:practice_sportsometimes 6.4978 8.3297
## parent_educsome college:practice_sportsometimes 2.7525 6.9253
## parent_educsome high school:practice_sportsometimes -1.5359 6.5116
## parent_educbachelor's degree:is_first_childyes 5.9213 4.8829
## parent_educhigh school:is_first_childyes 8.2978 4.1681
## parent_educmaster's degree:is_first_childyes 4.0575 7.2904
## parent_educsome college:is_first_childyes 11.3686 4.0703
## parent_educsome high school:is_first_childyes 6.6910 4.0992
## parent_educbachelor's degree:transport_meansschool_bus 2.9865 4.8745
## parent_educhigh school:transport_meansschool_bus 4.2359 3.8916
## parent_educmaster's degree:transport_meansschool_bus 7.9641 6.0004
## parent_educsome college:transport_meansschool_bus 2.9693 3.9628
## parent_educsome high school:transport_meansschool_bus 6.6974 4.0323
## parent_educbachelor's degree:wkly_study_hours> 10 -10.0969 7.1918
## parent_educhigh school:wkly_study_hours> 10 -8.9401 5.9867
## parent_educmaster's degree:wkly_study_hours> 10 -0.4929 12.9542
## parent_educsome college:wkly_study_hours> 10 -7.9346 6.0260
## parent_educsome high school:wkly_study_hours> 10 -9.2345 6.1375
## parent_educbachelor's degree:wkly_study_hours10-May -3.0831 4.9986
## parent_educhigh school:wkly_study_hours10-May -11.4380 4.6604
## parent_educmaster's degree:wkly_study_hours10-May -2.4586 6.6645
## parent_educsome college:wkly_study_hours10-May -4.9978 4.7455
## parent_educsome high school:wkly_study_hours10-May -9.0404 5.0069
## lunch_typestandard:test_prepnone -2.5751 2.9272
## lunch_typestandard:parent_marital_statusmarried -7.6602 3.8303
## lunch_typestandard:parent_marital_statussingle -4.8424 4.4351
## lunch_typestandard:parent_marital_statuswidowed -0.3401 75.8094
## lunch_typestandard:practice_sportregularly 9.3167 5.0489
## lunch_typestandard:practice_sportsometimes 11.9692 4.8670
## lunch_typestandard:is_first_childyes -3.2287 2.9659
## lunch_typestandard:transport_meansschool_bus -2.5877 2.7218
## lunch_typestandard:wkly_study_hours> 10 6.6183 4.1533
## lunch_typestandard:wkly_study_hours10-May 0.2394 3.1068
## test_prepnone:parent_marital_statusmarried 1.3790 3.8961
## test_prepnone:parent_marital_statussingle -2.2649 4.4856
## test_prepnone:parent_marital_statuswidowed -56.1241 39.6071
## test_prepnone:practice_sportregularly 2.1756 4.8701
## test_prepnone:practice_sportsometimes 4.8914 4.7728
## test_prepnone:is_first_childyes -0.6209 2.9395
## test_prepnone:transport_meansschool_bus 2.2476 2.6727
## test_prepnone:wkly_study_hours> 10 -2.8715 4.1954
## test_prepnone:wkly_study_hours10-May 2.5604 3.3110
## parent_marital_statusmarried:practice_sportregularly 4.6749 6.2606
## parent_marital_statussingle:practice_sportregularly -3.7080 8.1872
## parent_marital_statuswidowed:practice_sportregularly -2.7432 80.1680
## parent_marital_statusmarried:practice_sportsometimes 2.9212 6.1741
## parent_marital_statussingle:practice_sportsometimes -4.2724 8.0039
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -15.6491 4.6054
## parent_marital_statussingle:is_first_childyes -7.5649 5.1042
## parent_marital_statuswidowed:is_first_childyes 39.8253 28.4103
## parent_marital_statusmarried:transport_meansschool_bus 4.5994 3.8033
## parent_marital_statussingle:transport_meansschool_bus 0.4248 4.3343
## parent_marital_statuswidowed:transport_meansschool_bus -24.3230 18.4632
## parent_marital_statusmarried:wkly_study_hours> 10 19.5443 5.9414
## parent_marital_statussingle:wkly_study_hours> 10 25.1083 6.6075
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 5.3774 4.3617
## parent_marital_statussingle:wkly_study_hours10-May 7.7403 4.8173
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -5.8879 5.6556
## practice_sportsometimes:is_first_childyes -7.2854 5.5185
## practice_sportregularly:transport_meansschool_bus 9.5708 4.7258
## practice_sportsometimes:transport_meansschool_bus 6.1714 4.5868
## practice_sportregularly:wkly_study_hours> 10 5.1152 6.7000
## practice_sportsometimes:wkly_study_hours> 10 3.1990 6.5717
## practice_sportregularly:wkly_study_hours10-May 6.9393 5.1561
## practice_sportsometimes:wkly_study_hours10-May -0.3073 5.0837
## is_first_childyes:transport_meansschool_bus -3.0863 2.8768
## is_first_childyes:wkly_study_hours> 10 3.0112 4.3247
## is_first_childyes:wkly_study_hours10-May -2.5351 3.2646
## transport_meansschool_bus:wkly_study_hours> 10 2.0199 4.1559
## transport_meansschool_bus:wkly_study_hours10-May 1.8077 3.0009
## t value Pr(>|t|)
## (Intercept) 4.681 3.96e-06 ***
## gendermale -1.369 0.171871
## ethnic_groupgroup B -1.031 0.303382
## ethnic_groupgroup C -1.761 0.079032 .
## ethnic_groupgroup D -0.448 0.654545
## ethnic_groupgroup E -0.047 0.962465
## parent_educbachelor's degree 2.158 0.031556 *
## parent_educhigh school 0.719 0.472484
## parent_educmaster's degree -0.652 0.514593
## parent_educsome college -0.758 0.448740
## parent_educsome high school 0.033 0.973933
## lunch_typestandard 0.371 0.710536
## test_prepnone -2.153 0.031925 *
## parent_marital_statusmarried 1.442 0.150115
## parent_marital_statussingle 0.801 0.423760
## parent_marital_statuswidowed 1.099 0.272344
## practice_sportregularly -1.731 0.084330 .
## practice_sportsometimes -1.492 0.136489
## is_first_childyes 1.481 0.139442
## transport_meansschool_bus -0.381 0.703477
## wkly_study_hours> 10 -1.494 0.136054
## wkly_study_hours10-May 0.158 0.874530
## gendermale:ethnic_groupgroup B 0.822 0.411462
## gendermale:ethnic_groupgroup C 1.813 0.070644 .
## gendermale:ethnic_groupgroup D 1.138 0.255657
## gendermale:ethnic_groupgroup E 0.937 0.349605
## gendermale:parent_educbachelor's degree -0.707 0.479756
## gendermale:parent_educhigh school 0.290 0.772172
## gendermale:parent_educmaster's degree 1.576 0.115922
## gendermale:parent_educsome college -1.073 0.283958
## gendermale:parent_educsome high school 0.067 0.946710
## gendermale:lunch_typestandard -0.459 0.646819
## gendermale:test_prepnone -0.086 0.931825
## gendermale:parent_marital_statusmarried -0.129 0.897232
## gendermale:parent_marital_statussingle -0.036 0.971377
## gendermale:parent_marital_statuswidowed 0.071 0.943731
## gendermale:practice_sportregularly -0.689 0.491428
## gendermale:practice_sportsometimes -0.729 0.466204
## gendermale:is_first_childyes 1.108 0.268521
## gendermale:transport_meansschool_bus -0.061 0.951464
## gendermale:wkly_study_hours> 10 -0.971 0.332150
## gendermale:wkly_study_hours10-May -0.861 0.389706
## ethnic_groupgroup B:parent_educbachelor's degree -0.669 0.504113
## ethnic_groupgroup C:parent_educbachelor's degree -0.681 0.496462
## ethnic_groupgroup D:parent_educbachelor's degree -0.784 0.433391
## ethnic_groupgroup E:parent_educbachelor's degree -1.206 0.228465
## ethnic_groupgroup B:parent_educhigh school -2.074 0.038774 *
## ethnic_groupgroup C:parent_educhigh school -1.439 0.150891
## ethnic_groupgroup D:parent_educhigh school -1.003 0.316603
## ethnic_groupgroup E:parent_educhigh school -1.346 0.179020
## ethnic_groupgroup B:parent_educmaster's degree 0.327 0.743685
## ethnic_groupgroup C:parent_educmaster's degree -0.537 0.591656
## ethnic_groupgroup D:parent_educmaster's degree 0.205 0.837375
## ethnic_groupgroup E:parent_educmaster's degree 0.092 0.927013
## ethnic_groupgroup B:parent_educsome college 0.372 0.709764
## ethnic_groupgroup C:parent_educsome college 0.734 0.463358
## ethnic_groupgroup D:parent_educsome college 1.128 0.260175
## ethnic_groupgroup E:parent_educsome college 0.303 0.761758
## ethnic_groupgroup B:parent_educsome high school -2.148 0.032364 *
## ethnic_groupgroup C:parent_educsome high school -1.338 0.181530
## ethnic_groupgroup D:parent_educsome high school -0.854 0.393676
## ethnic_groupgroup E:parent_educsome high school -0.517 0.605302
## ethnic_groupgroup B:lunch_typestandard 0.563 0.573723
## ethnic_groupgroup C:lunch_typestandard 1.285 0.199701
## ethnic_groupgroup D:lunch_typestandard 0.722 0.470435
## ethnic_groupgroup E:lunch_typestandard -0.032 0.974675
## ethnic_groupgroup B:test_prepnone 0.428 0.669136
## ethnic_groupgroup C:test_prepnone 1.222 0.222374
## ethnic_groupgroup D:test_prepnone 0.805 0.421423
## ethnic_groupgroup E:test_prepnone 1.796 0.073229 .
## ethnic_groupgroup B:parent_marital_statusmarried 0.529 0.596832
## ethnic_groupgroup C:parent_marital_statusmarried -0.033 0.973967
## ethnic_groupgroup D:parent_marital_statusmarried -1.569 0.117469
## ethnic_groupgroup E:parent_marital_statusmarried -0.572 0.567873
## ethnic_groupgroup B:parent_marital_statussingle 1.163 0.245378
## ethnic_groupgroup C:parent_marital_statussingle 0.248 0.803994
## ethnic_groupgroup D:parent_marital_statussingle -0.322 0.747428
## ethnic_groupgroup E:parent_marital_statussingle 0.326 0.744500
## ethnic_groupgroup B:parent_marital_statuswidowed 0.728 0.466816
## ethnic_groupgroup C:parent_marital_statuswidowed 1.388 0.166042
## ethnic_groupgroup D:parent_marital_statuswidowed 0.146 0.884212
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.429 0.153942
## ethnic_groupgroup C:practice_sportregularly 1.587 0.113432
## ethnic_groupgroup D:practice_sportregularly 1.053 0.293000
## ethnic_groupgroup E:practice_sportregularly 1.260 0.208281
## ethnic_groupgroup B:practice_sportsometimes 1.166 0.244177
## ethnic_groupgroup C:practice_sportsometimes 2.096 0.036745 *
## ethnic_groupgroup D:practice_sportsometimes 1.043 0.297450
## ethnic_groupgroup E:practice_sportsometimes 1.184 0.237159
## ethnic_groupgroup B:is_first_childyes 1.732 0.084147 .
## ethnic_groupgroup C:is_first_childyes 0.650 0.516308
## ethnic_groupgroup D:is_first_childyes 0.347 0.728926
## ethnic_groupgroup E:is_first_childyes 0.447 0.654819
## ethnic_groupgroup B:transport_meansschool_bus -1.328 0.184937
## ethnic_groupgroup C:transport_meansschool_bus -2.169 0.030669 *
## ethnic_groupgroup D:transport_meansschool_bus -0.999 0.318358
## ethnic_groupgroup E:transport_meansschool_bus -1.970 0.049590 *
## ethnic_groupgroup B:wkly_study_hours> 10 -0.622 0.534294
## ethnic_groupgroup C:wkly_study_hours> 10 0.205 0.837996
## ethnic_groupgroup D:wkly_study_hours> 10 0.715 0.474919
## ethnic_groupgroup E:wkly_study_hours> 10 0.048 0.961392
## ethnic_groupgroup B:wkly_study_hours10-May -0.722 0.471008
## ethnic_groupgroup C:wkly_study_hours10-May 0.234 0.814802
## ethnic_groupgroup D:wkly_study_hours10-May 0.369 0.712263
## ethnic_groupgroup E:wkly_study_hours10-May -0.165 0.868800
## parent_educbachelor's degree:lunch_typestandard 0.205 0.837509
## parent_educhigh school:lunch_typestandard 0.250 0.803050
## parent_educmaster's degree:lunch_typestandard 0.975 0.329964
## parent_educsome college:lunch_typestandard 1.361 0.174329
## parent_educsome high school:lunch_typestandard 1.421 0.156247
## parent_educbachelor's degree:test_prepnone -0.294 0.768711
## parent_educhigh school:test_prepnone 0.432 0.666242
## parent_educmaster's degree:test_prepnone -0.303 0.761677
## parent_educsome college:test_prepnone -0.470 0.638759
## parent_educsome high school:test_prepnone 0.638 0.523982
## parent_educbachelor's degree:parent_marital_statusmarried -2.169 0.030688 *
## parent_educhigh school:parent_marital_statusmarried 0.459 0.646215
## parent_educmaster's degree:parent_marital_statusmarried 0.559 0.576337
## parent_educsome college:parent_marital_statusmarried -0.877 0.381080
## parent_educsome high school:parent_marital_statusmarried -0.703 0.482292
## parent_educbachelor's degree:parent_marital_statussingle -1.937 0.053489 .
## parent_educhigh school:parent_marital_statussingle 1.062 0.288837
## parent_educmaster's degree:parent_marital_statussingle 0.174 0.862019
## parent_educsome college:parent_marital_statussingle -0.758 0.448762
## parent_educsome high school:parent_marital_statussingle -0.619 0.536181
## parent_educbachelor's degree:parent_marital_statuswidowed -0.244 0.807209
## parent_educhigh school:parent_marital_statuswidowed -0.806 0.420742
## parent_educmaster's degree:parent_marital_statuswidowed -2.020 0.044071 *
## parent_educsome college:parent_marital_statuswidowed -1.435 0.152213
## parent_educsome high school:parent_marital_statuswidowed -0.846 0.398112
## parent_educbachelor's degree:practice_sportregularly 0.226 0.821088
## parent_educhigh school:practice_sportregularly -1.551 0.121650
## parent_educmaster's degree:practice_sportregularly 0.153 0.878559
## parent_educsome college:practice_sportregularly -0.021 0.983182
## parent_educsome high school:practice_sportregularly -0.471 0.637680
## parent_educbachelor's degree:practice_sportsometimes -1.060 0.289930
## parent_educhigh school:practice_sportsometimes -1.515 0.130609
## parent_educmaster's degree:practice_sportsometimes 0.780 0.435832
## parent_educsome college:practice_sportsometimes 0.397 0.691259
## parent_educsome high school:practice_sportsometimes -0.236 0.813660
## parent_educbachelor's degree:is_first_childyes 1.213 0.226003
## parent_educhigh school:is_first_childyes 1.991 0.047213 *
## parent_educmaster's degree:is_first_childyes 0.557 0.578162
## parent_educsome college:is_first_childyes 2.793 0.005483 **
## parent_educsome high school:is_first_childyes 1.632 0.103442
## parent_educbachelor's degree:transport_meansschool_bus 0.613 0.540462
## parent_educhigh school:transport_meansschool_bus 1.088 0.277080
## parent_educmaster's degree:transport_meansschool_bus 1.327 0.185211
## parent_educsome college:transport_meansschool_bus 0.749 0.454133
## parent_educsome high school:transport_meansschool_bus 1.661 0.097541 .
## parent_educbachelor's degree:wkly_study_hours> 10 -1.404 0.161148
## parent_educhigh school:wkly_study_hours> 10 -1.493 0.136173
## parent_educmaster's degree:wkly_study_hours> 10 -0.038 0.969667
## parent_educsome college:wkly_study_hours> 10 -1.317 0.188716
## parent_educsome high school:wkly_study_hours> 10 -1.505 0.133251
## parent_educbachelor's degree:wkly_study_hours10-May -0.617 0.537741
## parent_educhigh school:wkly_study_hours10-May -2.454 0.014560 *
## parent_educmaster's degree:wkly_study_hours10-May -0.369 0.712402
## parent_educsome college:wkly_study_hours10-May -1.053 0.292924
## parent_educsome high school:wkly_study_hours10-May -1.806 0.071766 .
## lunch_typestandard:test_prepnone -0.880 0.379567
## lunch_typestandard:parent_marital_statusmarried -2.000 0.046216 *
## lunch_typestandard:parent_marital_statussingle -1.092 0.275596
## lunch_typestandard:parent_marital_statuswidowed -0.004 0.996423
## lunch_typestandard:practice_sportregularly 1.845 0.065767 .
## lunch_typestandard:practice_sportsometimes 2.459 0.014363 *
## lunch_typestandard:is_first_childyes -1.089 0.277020
## lunch_typestandard:transport_meansschool_bus -0.951 0.342335
## lunch_typestandard:wkly_study_hours> 10 1.593 0.111876
## lunch_typestandard:wkly_study_hours10-May 0.077 0.938623
## test_prepnone:parent_marital_statusmarried 0.354 0.723573
## test_prepnone:parent_marital_statussingle -0.505 0.613893
## test_prepnone:parent_marital_statuswidowed -1.417 0.157290
## test_prepnone:practice_sportregularly 0.447 0.655333
## test_prepnone:practice_sportsometimes 1.025 0.306088
## test_prepnone:is_first_childyes -0.211 0.832828
## test_prepnone:transport_meansschool_bus 0.841 0.400913
## test_prepnone:wkly_study_hours> 10 -0.684 0.494109
## test_prepnone:wkly_study_hours10-May 0.773 0.439827
## parent_marital_statusmarried:practice_sportregularly 0.747 0.455689
## parent_marital_statussingle:practice_sportregularly -0.453 0.650870
## parent_marital_statuswidowed:practice_sportregularly -0.034 0.972721
## parent_marital_statusmarried:practice_sportsometimes 0.473 0.636383
## parent_marital_statussingle:practice_sportsometimes -0.534 0.593797
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -3.398 0.000750 ***
## parent_marital_statussingle:is_first_childyes -1.482 0.139140
## parent_marital_statuswidowed:is_first_childyes 1.402 0.161788
## parent_marital_statusmarried:transport_meansschool_bus 1.209 0.227285
## parent_marital_statussingle:transport_meansschool_bus 0.098 0.921980
## parent_marital_statuswidowed:transport_meansschool_bus -1.317 0.188500
## parent_marital_statusmarried:wkly_study_hours> 10 3.289 0.001097 **
## parent_marital_statussingle:wkly_study_hours> 10 3.800 0.000168 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 1.233 0.218380
## parent_marital_statussingle:wkly_study_hours10-May 1.607 0.108933
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -1.041 0.298498
## practice_sportsometimes:is_first_childyes -1.320 0.187560
## practice_sportregularly:transport_meansschool_bus 2.025 0.043539 *
## practice_sportsometimes:transport_meansschool_bus 1.345 0.179276
## practice_sportregularly:wkly_study_hours> 10 0.763 0.445653
## practice_sportsometimes:wkly_study_hours> 10 0.487 0.626687
## practice_sportregularly:wkly_study_hours10-May 1.346 0.179149
## practice_sportsometimes:wkly_study_hours10-May -0.060 0.951832
## is_first_childyes:transport_meansschool_bus -1.073 0.284019
## is_first_childyes:wkly_study_hours> 10 0.696 0.486682
## is_first_childyes:wkly_study_hours10-May -0.777 0.437906
## transport_meansschool_bus:wkly_study_hours> 10 0.486 0.627215
## transport_meansschool_bus:wkly_study_hours10-May 0.602 0.547281
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.42 on 383 degrees of freedom
## Multiple R-squared: 0.5844, Adjusted R-squared: 0.3608
## F-statistic: 2.614 on 206 and 383 DF, p-value: 2.56e-16stepwise_model_write <- step(full_fit_write, direction = "both", trace = 1)## Start: AIC=3131.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 245.4 59282 3123.9
## - ethnic_group:parent_educ 20 3361.8 62398 3124.1
## - gender:parent_marital_status 3 4.9 59041 3125.5
## - parent_educ:wkly_study_hours 10 1468.0 60504 3125.9
## - ethnic_group:wkly_study_hours 8 1092.4 60129 3126.2
## - parent_educ:transport_means 5 547.3 59583 3126.9
## - parent_marital_status:practice_sport 4 348.1 59384 3126.9
## - parent_educ:lunch_type 5 600.2 59636 3127.4
## - transport_means:wkly_study_hours 2 63.5 59100 3128.1
## - gender:practice_sport 2 85.6 59122 3128.3
## - ethnic_group:lunch_type 4 513.8 59550 3128.5
## - parent_educ:parent_marital_status 13 2409.8 61446 3129.0
## - gender:wkly_study_hours 2 167.8 59204 3129.1
## - gender:transport_means 1 0.6 59037 3129.4
## - gender:test_prep 1 1.1 59037 3129.4
## - test_prep:is_first_child 1 6.9 59043 3129.5
## - test_prep:parent_marital_status 2 211.7 59248 3129.5
## - gender:lunch_type 1 32.4 59069 3129.7
## - test_prep:practice_sport 2 244.8 59281 3129.8
## - gender:ethnic_group 4 652.4 59689 3129.9
## - gender:parent_educ 5 856.7 59893 3129.9
## - practice_sport:is_first_child 2 277.0 59313 3130.2
## - test_prep:transport_means 1 109.0 59145 3130.5
## - lunch_type:test_prep 1 119.3 59155 3130.6
## - lunch_type:transport_means 1 139.3 59176 3130.8
## - is_first_child:wkly_study_hours 2 340.9 59377 3130.8
## - ethnic_group:is_first_child 4 746.0 59782 3130.8
## - ethnic_group:test_prep 4 757.2 59793 3130.9
## - is_first_child:transport_means 1 177.4 59214 3131.2
## - lunch_type:is_first_child 1 182.7 59219 3131.2
## - ethnic_group:practice_sport 8 1610.3 60646 3131.3
## - gender:is_first_child 1 189.3 59225 3131.3
## - test_prep:wkly_study_hours 2 400.5 59437 3131.4
## <none> 59036 3131.4
## - parent_educ:practice_sport 10 2078.2 61114 3131.8
## - lunch_type:wkly_study_hours 2 509.7 59546 3132.5
## - parent_marital_status:transport_means 3 755.0 59791 3132.9
## - ethnic_group:parent_marital_status 9 1983.9 61020 3132.9
## - practice_sport:wkly_study_hours 4 995.1 60031 3133.3
## - lunch_type:parent_marital_status 2 650.3 59687 3133.9
## - practice_sport:transport_means 2 679.6 59716 3134.2
## - ethnic_group:transport_means 4 1108.7 60145 3134.4
## - parent_educ:is_first_child 5 1316.0 60352 3134.4
## - lunch_type:practice_sport 2 950.1 59986 3136.8
## - parent_marital_status:wkly_study_hours 4 2324.9 61361 3146.2
## - parent_marital_status:is_first_child 2 2312.7 61349 3150.1
##
## Step: AIC=3123.86
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3285.4 62567 3115.7
## - gender:parent_marital_status 3 7.5 59289 3117.9
## - ethnic_group:wkly_study_hours 8 1092.3 60374 3118.6
## - parent_marital_status:practice_sport 4 343.6 59625 3119.3
## - parent_educ:wkly_study_hours 10 1612.0 60894 3119.7
## - parent_educ:lunch_type 5 596.6 59878 3119.8
## - parent_educ:transport_means 5 601.4 59883 3119.8
## - transport_means:wkly_study_hours 2 57.6 59339 3120.4
## - gender:practice_sport 2 72.1 59354 3120.6
## - ethnic_group:lunch_type 4 535.1 59817 3121.2
## - parent_educ:parent_marital_status 13 2393.4 61675 3121.2
## - gender:wkly_study_hours 2 180.9 59462 3121.7
## - test_prep:parent_marital_status 2 184.5 59466 3121.7
## - gender:test_prep 1 0.0 59282 3121.9
## - gender:transport_means 1 1.8 59283 3121.9
## - test_prep:practice_sport 2 207.8 59489 3121.9
## - test_prep:is_first_child 1 10.7 59292 3122.0
## - gender:ethnic_group 4 627.6 59909 3122.1
## - gender:lunch_type 1 24.7 59306 3122.1
## - ethnic_group:test_prep 4 639.2 59921 3122.2
## - gender:parent_educ 5 892.7 60174 3122.7
## - test_prep:transport_means 1 98.8 59380 3122.8
## - is_first_child:wkly_study_hours 2 302.5 59584 3122.9
## - lunch_type:test_prep 1 116.0 59398 3123.0
## - practice_sport:is_first_child 2 323.8 59605 3123.1
## - lunch_type:transport_means 1 133.6 59415 3123.2
## - gender:is_first_child 1 166.6 59448 3123.5
## - ethnic_group:practice_sport 8 1607.5 60889 3123.6
## - ethnic_group:is_first_child 4 790.6 60072 3123.7
## - lunch_type:is_first_child 1 199.8 59481 3123.8
## <none> 59282 3123.9
## - is_first_child:transport_means 1 217.5 59499 3124.0
## - test_prep:wkly_study_hours 2 441.6 59723 3124.2
## - ethnic_group:parent_marital_status 9 1922.8 61204 3124.7
## - parent_educ:practice_sport 10 2157.5 61439 3124.9
## - lunch_type:wkly_study_hours 2 549.6 59831 3125.3
## - parent_marital_status:transport_means 3 758.5 60040 3125.4
## - lunch_type:parent_marital_status 2 587.8 59869 3125.7
## - practice_sport:wkly_study_hours 4 1017.6 60299 3125.9
## - ethnic_group:transport_means 4 1123.4 60405 3126.9
## - practice_sport:transport_means 2 729.9 60011 3127.1
## - parent_educ:is_first_child 5 1429.3 60711 3127.9
## - lunch_type:practice_sport 2 950.3 60232 3129.2
## + parent_educ:test_prep 5 245.4 59036 3131.4
## - parent_marital_status:wkly_study_hours 4 2425.4 61707 3139.5
## - parent_marital_status:is_first_child 2 2368.4 61650 3143.0
##
## Step: AIC=3115.68
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 838.3 63405 3107.5
## - parent_educ:wkly_study_hours 10 1310.7 63878 3107.9
## - gender:parent_marital_status 3 12.5 62579 3109.8
## - parent_educ:lunch_type 5 510.3 63077 3110.5
## - parent_marital_status:practice_sport 4 360.8 62928 3111.1
## - ethnic_group:practice_sport 8 1247.6 63815 3111.3
## - parent_educ:transport_means 5 641.0 63208 3111.7
## - gender:ethnic_group 4 522.4 63089 3112.6
## - ethnic_group:test_prep 4 527.3 63094 3112.6
## - test_prep:parent_marital_status 2 142.9 62710 3113.0
## - transport_means:wkly_study_hours 2 159.6 62726 3113.2
## - gender:wkly_study_hours 2 161.7 62729 3113.2
## - gender:parent_educ 5 828.0 63395 3113.4
## - gender:practice_sport 2 190.3 62757 3113.5
## - is_first_child:wkly_study_hours 2 192.2 62759 3113.5
## - gender:transport_means 1 0.9 62568 3113.7
## - gender:test_prep 1 1.5 62568 3113.7
## - lunch_type:test_prep 1 5.1 62572 3113.7
## - gender:lunch_type 1 8.8 62576 3113.8
## - test_prep:practice_sport 2 223.8 62791 3113.8
## - parent_educ:parent_marital_status 13 2624.7 65192 3113.9
## - gender:is_first_child 1 33.5 62600 3114.0
## - ethnic_group:lunch_type 4 675.1 63242 3114.0
## - test_prep:is_first_child 1 43.5 62610 3114.1
## - practice_sport:is_first_child 2 284.8 62852 3114.4
## - lunch_type:parent_marital_status 2 286.8 62854 3114.4
## - test_prep:transport_means 1 107.4 62674 3114.7
## - parent_educ:practice_sport 10 2081.2 64648 3115.0
## - is_first_child:transport_means 1 173.0 62740 3115.3
## - lunch_type:is_first_child 1 198.5 62765 3115.6
## - parent_marital_status:transport_means 3 631.4 63198 3115.6
## <none> 62567 3115.7
## - lunch_type:transport_means 1 233.7 62801 3115.9
## - test_prep:wkly_study_hours 2 483.1 63050 3116.2
## - ethnic_group:is_first_child 4 945.3 63512 3116.5
## - practice_sport:transport_means 2 532.5 63099 3116.7
## - ethnic_group:transport_means 4 994.0 63561 3117.0
## - practice_sport:wkly_study_hours 4 1093.7 63661 3117.9
## - ethnic_group:parent_marital_status 9 2217.3 64784 3118.2
## - parent_educ:is_first_child 5 1371.0 63938 3118.5
## - lunch_type:wkly_study_hours 2 842.3 63409 3119.6
## - lunch_type:practice_sport 2 1121.1 63688 3122.2
## + ethnic_group:parent_educ 20 3285.4 59282 3123.9
## + parent_educ:test_prep 5 169.0 62398 3124.1
## - parent_marital_status:wkly_study_hours 4 1981.5 64548 3126.1
## - parent_marital_status:is_first_child 2 2099.4 64666 3131.2
##
## Step: AIC=3107.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1414.74 64820 3100.6
## - gender:parent_marital_status 3 21.12 63426 3101.7
## - parent_marital_status:practice_sport 4 273.36 63679 3102.1
## - parent_educ:lunch_type 5 538.08 63943 3102.5
## - ethnic_group:practice_sport 8 1242.25 64647 3103.0
## - parent_educ:transport_means 5 629.09 64034 3103.4
## - transport_means:wkly_study_hours 2 74.29 63480 3104.2
## - gender:ethnic_group 4 521.25 63926 3104.4
## - ethnic_group:test_prep 4 528.77 63934 3104.4
## - parent_educ:parent_marital_status 13 2521.02 65926 3104.5
## - gender:wkly_study_hours 2 111.28 63517 3104.6
## - test_prep:parent_marital_status 2 160.78 63566 3105.0
## - gender:parent_educ 5 835.10 64240 3105.3
## - gender:practice_sport 2 198.93 63604 3105.4
## - is_first_child:wkly_study_hours 2 202.74 63608 3105.4
## - lunch_type:test_prep 1 0.02 63405 3105.5
## - gender:transport_means 1 1.41 63407 3105.6
## - test_prep:practice_sport 2 223.33 63629 3105.6
## - gender:lunch_type 1 9.19 63414 3105.6
## - gender:test_prep 1 10.73 63416 3105.6
## - gender:is_first_child 1 19.04 63424 3105.7
## - lunch_type:parent_marital_status 2 263.90 63669 3106.0
## - test_prep:is_first_child 1 61.13 63466 3106.1
## - test_prep:transport_means 1 83.82 63489 3106.3
## - ethnic_group:lunch_type 4 737.87 64143 3106.4
## - practice_sport:is_first_child 2 307.72 63713 3106.4
## - parent_educ:practice_sport 10 2084.34 65490 3106.6
## - is_first_child:transport_means 1 182.81 63588 3107.2
## - lunch_type:transport_means 1 190.55 63596 3107.3
## <none> 63405 3107.5
## - lunch_type:is_first_child 1 222.45 63628 3107.6
## - parent_marital_status:transport_means 3 668.96 64074 3107.7
## - ethnic_group:is_first_child 4 906.30 64312 3107.9
## - test_prep:wkly_study_hours 2 479.44 63885 3108.0
## - practice_sport:transport_means 2 522.81 63928 3108.4
## - ethnic_group:transport_means 4 1002.86 64408 3108.8
## - ethnic_group:parent_marital_status 9 2134.54 65540 3109.1
## - parent_educ:is_first_child 5 1308.56 64714 3109.6
## - practice_sport:wkly_study_hours 4 1141.24 64546 3110.1
## - lunch_type:wkly_study_hours 2 905.28 64311 3111.9
## - lunch_type:practice_sport 2 1150.67 64556 3114.2
## + ethnic_group:wkly_study_hours 8 838.30 62567 3115.7
## + parent_educ:test_prep 5 193.76 63211 3115.7
## - parent_marital_status:wkly_study_hours 4 1837.59 65243 3116.4
## + ethnic_group:parent_educ 20 3031.37 60374 3118.6
## - parent_marital_status:is_first_child 2 1979.54 65385 3121.7
##
## Step: AIC=3100.56
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 8.23 64828 3094.6
## - parent_educ:lunch_type 5 450.88 65271 3094.7
## - ethnic_group:practice_sport 8 1175.09 65995 3095.2
## - parent_marital_status:practice_sport 4 329.09 65149 3095.5
## - parent_educ:transport_means 5 709.12 65529 3097.0
## - gender:ethnic_group 4 488.42 65308 3097.0
## - ethnic_group:test_prep 4 513.16 65333 3097.2
## - transport_means:wkly_study_hours 2 111.53 64932 3097.6
## - gender:parent_educ 5 786.39 65606 3097.7
## - test_prep:parent_marital_status 2 128.82 64949 3097.7
## - is_first_child:wkly_study_hours 2 153.41 64973 3097.9
## - ethnic_group:lunch_type 4 608.64 65429 3098.1
## - gender:practice_sport 2 169.79 64990 3098.1
## - gender:transport_means 1 0.57 64821 3098.6
## - lunch_type:test_prep 1 2.61 64823 3098.6
## - gender:wkly_study_hours 2 223.32 65043 3098.6
## - practice_sport:is_first_child 2 227.73 65048 3098.6
## - gender:lunch_type 1 9.90 64830 3098.7
## - gender:test_prep 1 17.01 64837 3098.7
## - gender:is_first_child 1 29.46 64849 3098.8
## - test_prep:is_first_child 1 46.22 64866 3099.0
## - test_prep:practice_sport 2 284.13 65104 3099.1
## - lunch_type:parent_marital_status 2 297.47 65117 3099.3
## - test_prep:transport_means 1 90.44 64910 3099.4
## - parent_educ:parent_marital_status 13 2797.67 67618 3099.5
## - lunch_type:is_first_child 1 167.64 64988 3100.1
## - practice_sport:transport_means 2 388.54 65209 3100.1
## - is_first_child:transport_means 1 187.17 65007 3100.3
## <none> 64820 3100.6
## - ethnic_group:transport_means 4 890.45 65710 3100.6
## - practice_sport:wkly_study_hours 4 895.41 65715 3100.7
## - lunch_type:transport_means 1 231.07 65051 3100.7
## - parent_marital_status:transport_means 3 689.01 65509 3100.8
## - parent_educ:practice_sport 10 2285.42 67105 3101.0
## - ethnic_group:is_first_child 4 941.18 65761 3101.1
## - test_prep:wkly_study_hours 2 567.28 65387 3101.7
## - parent_educ:is_first_child 5 1260.35 66080 3101.9
## - lunch_type:wkly_study_hours 2 732.64 65553 3103.2
## - ethnic_group:parent_marital_status 9 2313.61 67134 3103.2
## - lunch_type:practice_sport 2 1122.55 65943 3106.7
## + parent_educ:wkly_study_hours 10 1414.74 63405 3107.5
## + ethnic_group:wkly_study_hours 8 942.30 63878 3107.9
## + parent_educ:test_prep 5 254.90 64565 3108.2
## - parent_marital_status:wkly_study_hours 4 2025.70 66846 3110.7
## + ethnic_group:parent_educ 20 2750.70 62069 3115.0
## - parent_marital_status:is_first_child 2 2080.59 66901 3115.2
##
## Step: AIC=3094.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:lunch_type + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 453.76 65282 3088.8
## - ethnic_group:practice_sport 8 1171.59 66000 3089.2
## - parent_marital_status:practice_sport 4 327.63 65156 3089.6
## - parent_educ:transport_means 5 704.99 65533 3091.0
## - gender:ethnic_group 4 484.60 65313 3091.0
## - ethnic_group:test_prep 4 518.12 65346 3091.3
## - transport_means:wkly_study_hours 2 112.25 64940 3091.7
## - test_prep:parent_marital_status 2 129.44 64958 3091.8
## - gender:parent_educ 5 802.53 65631 3091.9
## - is_first_child:wkly_study_hours 2 150.98 64979 3092.0
## - ethnic_group:lunch_type 4 611.63 65440 3092.2
## - gender:practice_sport 2 175.34 65004 3092.2
## - gender:transport_means 1 0.68 64829 3092.6
## - lunch_type:test_prep 1 2.43 64831 3092.7
## - practice_sport:is_first_child 2 227.81 65056 3092.7
## - gender:lunch_type 1 9.03 64837 3092.7
## - gender:wkly_study_hours 2 232.70 65061 3092.7
## - gender:test_prep 1 17.92 64846 3092.8
## - gender:is_first_child 1 32.58 64861 3092.9
## - test_prep:is_first_child 1 46.46 64875 3093.1
## - test_prep:practice_sport 2 295.19 65123 3093.3
## - test_prep:transport_means 1 89.71 64918 3093.4
## - lunch_type:parent_marital_status 2 325.21 65153 3093.6
## - parent_educ:parent_marital_status 13 2846.27 67674 3094.0
## - practice_sport:transport_means 2 384.18 65212 3094.1
## - lunch_type:is_first_child 1 169.80 64998 3094.2
## - is_first_child:transport_means 1 197.72 65026 3094.4
## <none> 64828 3094.6
## - ethnic_group:transport_means 4 891.25 65719 3094.7
## - lunch_type:transport_means 1 237.39 65066 3094.8
## - practice_sport:wkly_study_hours 4 914.03 65742 3094.9
## - ethnic_group:is_first_child 4 941.88 65770 3095.1
## - parent_educ:practice_sport 10 2323.35 67152 3095.4
## - test_prep:wkly_study_hours 2 565.73 65394 3095.8
## - parent_marital_status:transport_means 3 799.54 65628 3095.9
## - parent_educ:is_first_child 5 1262.58 66091 3096.0
## - lunch_type:wkly_study_hours 2 745.49 65574 3097.4
## - ethnic_group:parent_marital_status 9 2441.41 67270 3098.4
## + gender:parent_marital_status 3 8.23 64820 3100.6
## - lunch_type:practice_sport 2 1165.09 65993 3101.1
## + parent_educ:wkly_study_hours 10 1401.85 63426 3101.7
## + ethnic_group:wkly_study_hours 8 943.83 63884 3102.0
## + parent_educ:test_prep 5 256.20 64572 3102.3
## - parent_marital_status:wkly_study_hours 4 2029.22 66857 3104.8
## + ethnic_group:parent_educ 20 2749.68 62079 3109.1
## - parent_marital_status:is_first_child 2 2115.57 66944 3109.6
##
## Step: AIC=3088.75
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1102.72 66385 3082.6
## - parent_marital_status:practice_sport 4 362.52 65644 3084.0
## - gender:ethnic_group 4 473.96 65756 3085.0
## - parent_educ:transport_means 5 705.99 65988 3085.1
## - gender:parent_educ 5 730.18 66012 3085.3
## - ethnic_group:test_prep 4 552.03 65834 3085.7
## - test_prep:parent_marital_status 2 124.91 65407 3085.9
## - transport_means:wkly_study_hours 2 125.88 65408 3085.9
## - ethnic_group:lunch_type 4 589.22 65871 3086.1
## - is_first_child:wkly_study_hours 2 147.84 65430 3086.1
## - gender:practice_sport 2 177.50 65459 3086.3
## - gender:wkly_study_hours 2 210.11 65492 3086.6
## - gender:transport_means 1 0.48 65282 3086.8
## - lunch_type:test_prep 1 3.83 65286 3086.8
## - gender:test_prep 1 15.37 65297 3086.9
## - practice_sport:is_first_child 2 240.28 65522 3086.9
## - gender:lunch_type 1 24.06 65306 3087.0
## - test_prep:is_first_child 1 34.65 65317 3087.1
## - gender:is_first_child 1 64.33 65346 3087.3
## - lunch_type:parent_marital_status 2 294.12 65576 3087.4
## - test_prep:transport_means 1 113.55 65396 3087.8
## - test_prep:practice_sport 2 351.93 65634 3087.9
## - lunch_type:is_first_child 1 140.20 65422 3088.0
## - ethnic_group:transport_means 4 848.96 66131 3088.4
## - is_first_child:transport_means 1 183.22 65465 3088.4
## <none> 65282 3088.8
## - practice_sport:transport_means 2 445.89 65728 3088.8
## - parent_educ:parent_marital_status 13 2963.47 68245 3088.9
## - lunch_type:transport_means 1 274.34 65556 3089.2
## - ethnic_group:is_first_child 4 953.00 66235 3089.3
## - practice_sport:wkly_study_hours 4 967.93 66250 3089.4
## - parent_educ:practice_sport 10 2339.85 67622 3089.5
## - parent_educ:is_first_child 5 1226.98 66509 3089.7
## - test_prep:wkly_study_hours 2 569.64 65852 3089.9
## - parent_marital_status:transport_means 3 859.31 66141 3090.5
## - lunch_type:wkly_study_hours 2 714.94 65997 3091.2
## - ethnic_group:parent_marital_status 9 2385.39 67667 3091.9
## + parent_educ:lunch_type 5 453.76 64828 3094.6
## + gender:parent_marital_status 3 11.11 65271 3094.7
## - lunch_type:practice_sport 2 1117.40 66399 3094.8
## + ethnic_group:wkly_study_hours 8 944.83 64337 3096.1
## + parent_educ:wkly_study_hours 10 1311.24 63971 3096.8
## + parent_educ:test_prep 5 207.94 65074 3096.9
## - parent_marital_status:wkly_study_hours 4 2112.97 67395 3099.5
## + ethnic_group:parent_educ 20 2782.22 62500 3103.1
## - parent_marital_status:is_first_child 2 2274.32 67556 3104.9
##
## Step: AIC=3082.63
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 334.06 66719 3077.6
## - parent_educ:transport_means 5 602.59 66987 3078.0
## - gender:parent_educ 5 667.19 67052 3078.5
## - parent_marital_status:practice_sport 4 536.65 66921 3079.4
## - ethnic_group:test_prep 4 578.24 66963 3079.8
## - practice_sport:is_first_child 2 144.13 66529 3079.9
## - test_prep:parent_marital_status 2 152.27 66537 3080.0
## - transport_means:wkly_study_hours 2 160.57 66545 3080.1
## - is_first_child:wkly_study_hours 2 164.84 66550 3080.1
## - gender:transport_means 1 1.29 66386 3080.6
## - gender:test_prep 1 5.51 66390 3080.7
## - gender:lunch_type 1 10.61 66395 3080.7
## - ethnic_group:lunch_type 4 704.57 67089 3080.9
## - test_prep:is_first_child 1 28.20 66413 3080.9
## - gender:is_first_child 1 30.57 66415 3080.9
## - lunch_type:test_prep 1 31.63 66416 3080.9
## - test_prep:practice_sport 2 289.60 66674 3081.2
## - gender:wkly_study_hours 2 292.89 66678 3081.2
## - lunch_type:parent_marital_status 2 313.74 66698 3081.4
## - parent_educ:parent_marital_status 13 2856.05 69241 3081.5
## - gender:practice_sport 2 329.64 66714 3081.6
## - test_prep:transport_means 1 123.71 66508 3081.7
## - ethnic_group:is_first_child 4 851.65 67236 3082.2
## - ethnic_group:transport_means 4 854.21 67239 3082.2
## - lunch_type:is_first_child 1 178.29 66563 3082.2
## - practice_sport:transport_means 2 413.68 66798 3082.3
## - lunch_type:transport_means 1 210.36 66595 3082.5
## <none> 66385 3082.6
## - is_first_child:transport_means 1 226.07 66611 3082.6
## - test_prep:wkly_study_hours 2 457.36 66842 3082.7
## - practice_sport:wkly_study_hours 4 926.35 67311 3082.8
## - parent_educ:practice_sport 10 2400.56 68785 3083.6
## - parent_educ:is_first_child 5 1378.21 67763 3084.8
## - parent_marital_status:transport_means 3 938.11 67323 3084.9
## - lunch_type:wkly_study_hours 2 734.78 67119 3085.1
## - ethnic_group:parent_marital_status 9 2431.75 68816 3085.8
## - lunch_type:practice_sport 2 1041.78 67426 3087.8
## + gender:parent_marital_status 3 8.49 66376 3088.6
## + ethnic_group:practice_sport 8 1102.72 65282 3088.8
## + parent_educ:lunch_type 5 384.89 66000 3089.2
## + ethnic_group:wkly_study_hours 8 970.65 65414 3089.9
## + parent_educ:test_prep 5 200.85 66184 3090.8
## + parent_educ:wkly_study_hours 10 1239.53 65145 3091.5
## - parent_marital_status:wkly_study_hours 4 2251.07 68636 3094.3
## - parent_marital_status:is_first_child 2 2096.19 68481 3097.0
## + ethnic_group:parent_educ 20 2346.89 64038 3101.4
##
## Step: AIC=3077.59
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 543.87 67263 3072.4
## - gender:parent_educ 5 573.95 67293 3072.6
## - ethnic_group:test_prep 4 502.89 67222 3074.0
## - parent_marital_status:practice_sport 4 539.12 67258 3074.3
## - test_prep:parent_marital_status 2 143.84 66863 3074.9
## - is_first_child:wkly_study_hours 2 166.05 66885 3075.1
## - practice_sport:is_first_child 2 168.91 66888 3075.1
## - transport_means:wkly_study_hours 2 184.33 66903 3075.2
## - gender:transport_means 1 0.05 66719 3075.6
## - gender:test_prep 1 4.59 66723 3075.6
## - gender:lunch_type 1 8.88 66728 3075.7
## - ethnic_group:lunch_type 4 701.29 67420 3075.8
## - test_prep:is_first_child 1 27.50 66746 3075.8
## - gender:is_first_child 1 37.57 66756 3075.9
## - lunch_type:test_prep 1 42.48 66761 3076.0
## - test_prep:practice_sport 2 284.58 67003 3076.1
## - lunch_type:parent_marital_status 2 300.95 67020 3076.2
## - gender:practice_sport 2 316.56 67035 3076.4
## - gender:wkly_study_hours 2 323.72 67042 3076.4
## - test_prep:transport_means 1 136.37 66855 3076.8
## - parent_educ:parent_marital_status 13 2927.80 69647 3076.9
## - ethnic_group:is_first_child 4 837.49 67556 3076.9
## - ethnic_group:transport_means 4 843.50 67562 3077.0
## - practice_sport:transport_means 2 404.91 67124 3077.2
## - lunch_type:is_first_child 1 185.14 66904 3077.2
## - lunch_type:transport_means 1 215.15 66934 3077.5
## <none> 66719 3077.6
## - is_first_child:transport_means 1 247.01 66966 3077.8
## - test_prep:wkly_study_hours 2 499.70 67218 3078.0
## - practice_sport:wkly_study_hours 4 963.49 67682 3078.1
## - parent_educ:practice_sport 10 2429.40 69148 3078.7
## - ethnic_group:parent_marital_status 9 2321.43 69040 3079.8
## - parent_marital_status:transport_means 3 952.44 67671 3079.9
## - lunch_type:wkly_study_hours 2 735.88 67455 3080.1
## - parent_educ:is_first_child 5 1473.91 68193 3080.5
## + gender:ethnic_group 4 334.06 66385 3082.6
## + gender:parent_marital_status 3 9.39 66709 3083.5
## - lunch_type:practice_sport 2 1175.07 67894 3083.9
## + parent_educ:lunch_type 5 385.08 66334 3084.2
## + ethnic_group:wkly_study_hours 8 973.05 65746 3084.9
## + ethnic_group:practice_sport 8 962.81 65756 3085.0
## + parent_educ:test_prep 5 159.07 66560 3086.2
## + parent_educ:wkly_study_hours 10 1225.64 65493 3086.7
## - parent_marital_status:wkly_study_hours 4 2289.79 69009 3089.5
## - parent_marital_status:is_first_child 2 2193.29 68912 3092.7
## + ethnic_group:parent_educ 20 2280.02 64439 3097.1
##
## Step: AIC=3072.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 579.12 67842 3067.4
## - ethnic_group:test_prep 4 537.48 67800 3069.1
## - parent_marital_status:practice_sport 4 539.25 67802 3069.1
## - test_prep:parent_marital_status 2 134.95 67398 3069.6
## - practice_sport:is_first_child 2 135.32 67398 3069.6
## - is_first_child:wkly_study_hours 2 153.61 67416 3069.7
## - transport_means:wkly_study_hours 2 184.05 67447 3070.0
## - gender:transport_means 1 0.09 67263 3070.4
## - gender:test_prep 1 1.81 67264 3070.4
## - gender:lunch_type 1 15.08 67278 3070.5
## - gender:is_first_child 1 33.95 67297 3070.7
## - gender:wkly_study_hours 2 266.92 67530 3070.7
## - test_prep:is_first_child 1 50.08 67313 3070.8
## - lunch_type:test_prep 1 58.79 67321 3070.9
## - test_prep:practice_sport 2 301.02 67564 3071.0
## - ethnic_group:lunch_type 4 765.58 68028 3071.1
## - practice_sport:transport_means 2 331.21 67594 3071.3
## - parent_educ:parent_marital_status 13 2920.47 70183 3071.5
## - gender:practice_sport 2 354.13 67617 3071.5
## - lunch_type:parent_marital_status 2 356.61 67619 3071.5
## - test_prep:transport_means 1 161.49 67424 3071.8
## - ethnic_group:is_first_child 4 860.27 68123 3071.9
## - lunch_type:is_first_child 1 192.18 67455 3072.1
## - is_first_child:transport_means 1 210.90 67474 3072.2
## - lunch_type:transport_means 1 213.26 67476 3072.2
## <none> 67263 3072.4
## - ethnic_group:transport_means 4 960.94 68224 3072.8
## - test_prep:wkly_study_hours 2 521.24 67784 3072.9
## - parent_educ:practice_sport 10 2393.16 69656 3073.0
## - practice_sport:wkly_study_hours 4 1070.29 68333 3073.7
## - parent_marital_status:transport_means 3 845.76 68108 3073.8
## - parent_educ:is_first_child 5 1453.38 68716 3075.0
## - ethnic_group:parent_marital_status 9 2419.49 69682 3075.2
## - lunch_type:wkly_study_hours 2 855.76 68118 3075.8
## + parent_educ:transport_means 5 543.87 66719 3077.6
## + gender:ethnic_group 4 275.34 66987 3078.0
## + gender:parent_marital_status 3 15.46 67247 3078.2
## + parent_educ:lunch_type 5 384.38 66878 3079.0
## - lunch_type:practice_sport 2 1273.57 68536 3079.4
## + ethnic_group:wkly_study_hours 8 916.36 66346 3080.3
## + parent_educ:test_prep 5 205.37 67057 3080.6
## + ethnic_group:practice_sport 8 878.28 66384 3080.6
## + parent_educ:wkly_study_hours 10 1247.47 66015 3081.3
## - parent_marital_status:wkly_study_hours 4 2322.31 69585 3084.4
## - parent_marital_status:is_first_child 2 2177.48 69440 3087.2
## + ethnic_group:parent_educ 20 2463.59 64799 3090.4
##
## Step: AIC=3067.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 472.9 68315 3063.5
## - parent_marital_status:practice_sport 4 538.6 68380 3064.1
## - test_prep:parent_marital_status 2 116.3 67958 3064.4
## - practice_sport:is_first_child 2 164.3 68006 3064.9
## - is_first_child:wkly_study_hours 2 175.1 68017 3065.0
## - transport_means:wkly_study_hours 2 188.2 68030 3065.1
## - gender:transport_means 1 0.1 67842 3065.4
## - gender:test_prep 1 1.5 67843 3065.4
## - ethnic_group:lunch_type 4 700.2 68542 3065.5
## - gender:lunch_type 1 16.1 67858 3065.6
## - gender:is_first_child 1 34.3 67876 3065.7
## - gender:wkly_study_hours 2 295.8 68138 3066.0
## - practice_sport:transport_means 2 303.3 68145 3066.1
## - test_prep:is_first_child 1 73.1 67915 3066.1
## - lunch_type:test_prep 1 80.4 67922 3066.1
## - lunch_type:parent_marital_status 2 345.7 68187 3066.4
## - test_prep:practice_sport 2 352.4 68194 3066.5
## - gender:practice_sport 2 362.5 68204 3066.6
## - test_prep:transport_means 1 158.6 68000 3066.8
## - ethnic_group:is_first_child 4 855.9 68698 3066.8
## - is_first_child:transport_means 1 195.1 68037 3067.1
## - lunch_type:is_first_child 1 204.2 68046 3067.2
## <none> 67842 3067.4
## - parent_educ:practice_sport 10 2394.3 70236 3067.9
## - lunch_type:transport_means 1 288.9 68131 3067.9
## - test_prep:wkly_study_hours 2 576.3 68418 3068.4
## - practice_sport:wkly_study_hours 4 1062.6 68904 3068.6
## - parent_educ:is_first_child 5 1333.5 69175 3068.9
## - parent_educ:parent_marital_status 13 3262.6 71104 3069.2
## - ethnic_group:transport_means 4 1140.1 68982 3069.3
## - parent_marital_status:transport_means 3 926.1 68768 3069.4
## - ethnic_group:parent_marital_status 9 2363.8 70206 3069.7
## - lunch_type:wkly_study_hours 2 879.5 68721 3071.0
## + gender:parent_educ 5 579.1 67263 3072.4
## + parent_educ:transport_means 5 549.0 67293 3072.6
## + gender:parent_marital_status 3 4.7 67837 3073.4
## + gender:ethnic_group 4 194.0 67648 3073.8
## + parent_educ:lunch_type 5 343.0 67499 3074.4
## - lunch_type:practice_sport 2 1328.3 69170 3074.9
## + ethnic_group:wkly_study_hours 8 895.6 66946 3075.6
## + parent_educ:test_prep 5 172.0 67670 3075.9
## + ethnic_group:practice_sport 8 845.9 66996 3076.0
## + parent_educ:wkly_study_hours 10 1223.0 66619 3076.7
## - parent_marital_status:wkly_study_hours 4 2407.9 70250 3080.0
## - parent_marital_status:is_first_child 2 2111.7 69953 3081.5
## + ethnic_group:parent_educ 20 2467.1 65375 3085.6
##
## Step: AIC=3063.54
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 515.8 68830 3060.0
## - test_prep:parent_marital_status 2 135.4 68450 3060.7
## - ethnic_group:lunch_type 4 622.0 68937 3060.9
## - is_first_child:wkly_study_hours 2 165.2 68480 3061.0
## - transport_means:wkly_study_hours 2 186.3 68501 3061.1
## - practice_sport:is_first_child 2 200.7 68515 3061.3
## - gender:test_prep 1 0.1 68315 3061.5
## - gender:transport_means 1 0.1 68315 3061.5
## - gender:lunch_type 1 9.7 68324 3061.6
## - gender:is_first_child 1 17.5 68332 3061.7
## - test_prep:practice_sport 2 287.2 68602 3062.0
## - test_prep:is_first_child 1 69.2 68384 3062.1
## - gender:wkly_study_hours 2 303.9 68619 3062.2
## - practice_sport:transport_means 2 316.7 68631 3062.3
## - lunch_type:test_prep 1 103.0 68418 3062.4
## - gender:practice_sport 2 362.7 68677 3062.7
## - lunch_type:parent_marital_status 2 373.3 68688 3062.8
## - ethnic_group:is_first_child 4 849.9 69165 3062.8
## - test_prep:transport_means 1 196.2 68511 3063.2
## - is_first_child:transport_means 1 200.9 68515 3063.3
## - lunch_type:is_first_child 1 207.4 68522 3063.3
## <none> 68315 3063.5
## - parent_educ:practice_sport 10 2386.3 70701 3063.8
## - lunch_type:transport_means 1 325.6 68640 3064.3
## - practice_sport:wkly_study_hours 4 1079.2 69394 3064.8
## - parent_educ:is_first_child 5 1328.6 69643 3064.9
## - test_prep:wkly_study_hours 2 642.6 68957 3065.1
## - parent_educ:parent_marital_status 13 3270.8 71585 3065.1
## - parent_marital_status:transport_means 3 893.5 69208 3065.2
## - ethnic_group:parent_marital_status 9 2398.8 70713 3065.9
## - ethnic_group:transport_means 4 1216.2 69531 3065.9
## - lunch_type:wkly_study_hours 2 883.9 69199 3067.1
## + ethnic_group:test_prep 4 472.9 67842 3067.4
## + parent_educ:transport_means 5 580.8 67734 3068.5
## + gender:parent_educ 5 514.5 67800 3069.1
## + gender:parent_marital_status 3 4.7 68310 3069.5
## + gender:ethnic_group 4 157.4 68157 3070.2
## + parent_educ:lunch_type 5 352.3 67962 3070.5
## + ethnic_group:wkly_study_hours 8 891.3 67423 3071.8
## - lunch_type:practice_sport 2 1447.4 69762 3071.9
## + ethnic_group:practice_sport 8 870.0 67445 3072.0
## + parent_educ:wkly_study_hours 10 1235.0 67080 3072.8
## + parent_educ:test_prep 5 87.1 68228 3072.8
## - parent_marital_status:wkly_study_hours 4 2256.3 70571 3074.7
## - parent_marital_status:is_first_child 2 2108.8 70423 3077.5
## + ethnic_group:parent_educ 20 2467.3 65847 3081.8
##
## Step: AIC=3059.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 2 118.5 68949 3057.0
## - practice_sport:is_first_child 2 135.1 68966 3057.1
## - lunch_type:parent_marital_status 3 380.8 69211 3057.2
## - transport_means:wkly_study_hours 2 180.1 69011 3057.5
## - is_first_child:wkly_study_hours 2 208.2 69039 3057.8
## - ethnic_group:lunch_type 4 693.2 69524 3057.9
## - gender:transport_means 1 0.1 68831 3058.0
## - gender:test_prep 1 1.6 68832 3058.0
## - gender:is_first_child 1 10.6 68841 3058.1
## - gender:lunch_type 1 11.7 68842 3058.1
## - practice_sport:transport_means 2 277.5 69108 3058.3
## - test_prep:practice_sport 2 288.4 69119 3058.4
## - test_prep:is_first_child 1 63.3 68894 3058.5
## - gender:wkly_study_hours 2 335.4 69166 3058.8
## - lunch_type:test_prep 1 108.8 68939 3058.9
## - lunch_type:is_first_child 1 147.8 68978 3059.2
## - ethnic_group:is_first_child 4 868.0 69698 3059.4
## - gender:practice_sport 2 400.2 69231 3059.4
## - test_prep:transport_means 1 173.0 69003 3059.5
## - parent_educ:practice_sport 10 2335.4 71166 3059.7
## - is_first_child:transport_means 1 222.7 69053 3059.9
## <none> 68830 3060.0
## - lunch_type:transport_means 1 270.9 69101 3060.3
## - ethnic_group:parent_marital_status 10 2412.2 71243 3060.3
## - parent_educ:is_first_child 5 1324.6 70155 3061.2
## - practice_sport:wkly_study_hours 4 1108.8 69939 3061.4
## - parent_marital_status:transport_means 3 877.4 69708 3061.4
## - ethnic_group:transport_means 4 1123.2 69954 3061.5
## - test_prep:wkly_study_hours 2 713.3 69544 3062.1
## - parent_educ:parent_marital_status 14 3646.4 72477 3062.4
## - lunch_type:wkly_study_hours 2 867.7 69698 3063.4
## + parent_marital_status:practice_sport 4 515.8 68315 3063.5
## + ethnic_group:test_prep 4 450.1 68380 3064.1
## + parent_educ:transport_means 5 597.6 68233 3064.8
## + gender:parent_educ 5 512.3 68318 3065.6
## + gender:parent_marital_status 3 3.7 68827 3065.9
## + gender:ethnic_group 4 171.0 68659 3066.5
## + parent_educ:lunch_type 5 376.4 68454 3066.7
## + ethnic_group:practice_sport 8 991.3 67839 3067.4
## - lunch_type:practice_sport 2 1394.4 70225 3067.8
## + parent_educ:wkly_study_hours 10 1326.5 67504 3068.5
## + parent_educ:test_prep 5 91.2 68739 3069.2
## + ethnic_group:wkly_study_hours 8 764.8 68066 3069.4
## - parent_marital_status:wkly_study_hours 5 2336.3 71167 3069.7
## - parent_marital_status:is_first_child 2 2343.8 71174 3075.7
## + ethnic_group:parent_educ 20 2528.6 66302 3077.9
##
## Step: AIC=3056.99
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 363.1 69312 3054.1
## - practice_sport:is_first_child 2 128.7 69078 3054.1
## - transport_means:wkly_study_hours 2 187.6 69137 3054.6
## - is_first_child:wkly_study_hours 2 219.9 69169 3054.9
## - gender:transport_means 1 0.0 68949 3055.0
## - gender:test_prep 1 0.9 68950 3055.0
## - ethnic_group:lunch_type 4 708.8 69658 3055.0
## - gender:is_first_child 1 12.3 68961 3055.1
## - gender:lunch_type 1 13.4 68962 3055.1
## - practice_sport:transport_means 2 279.0 69228 3055.4
## - test_prep:practice_sport 2 309.6 69259 3055.6
## - test_prep:is_first_child 1 81.0 69030 3055.7
## - gender:wkly_study_hours 2 339.7 69289 3055.9
## - ethnic_group:parent_marital_status 11 2493.0 71442 3055.9
## - lunch_type:test_prep 1 116.7 69066 3056.0
## - lunch_type:is_first_child 1 130.3 69079 3056.1
## - gender:practice_sport 2 390.2 69339 3056.3
## - test_prep:transport_means 1 190.2 69139 3056.6
## - parent_educ:practice_sport 10 2364.1 71313 3056.9
## - is_first_child:transport_means 1 221.4 69170 3056.9
## <none> 68949 3057.0
## - ethnic_group:is_first_child 4 941.5 69890 3057.0
## - lunch_type:transport_means 1 271.5 69221 3057.3
## - practice_sport:wkly_study_hours 4 1068.4 70017 3058.1
## - parent_educ:parent_marital_status 15 3736.4 72685 3058.1
## - parent_educ:is_first_child 5 1326.1 70275 3058.2
## - ethnic_group:transport_means 4 1133.8 70083 3058.6
## - parent_marital_status:transport_means 3 949.4 69898 3059.1
## - test_prep:wkly_study_hours 2 717.9 69667 3059.1
## + test_prep:parent_marital_status 2 118.5 68830 3060.0
## - lunch_type:wkly_study_hours 2 854.3 69803 3060.3
## + parent_marital_status:practice_sport 4 498.9 68450 3060.7
## + ethnic_group:test_prep 4 471.9 68477 3060.9
## + parent_educ:transport_means 5 594.1 68355 3061.9
## + gender:parent_educ 5 487.7 68461 3062.8
## + gender:parent_marital_status 3 3.2 68946 3063.0
## + gender:ethnic_group 4 173.1 68776 3063.5
## + parent_educ:lunch_type 5 381.0 68568 3063.7
## + ethnic_group:practice_sport 8 1010.9 67938 3064.3
## - lunch_type:practice_sport 2 1364.2 70313 3064.6
## + parent_educ:wkly_study_hours 10 1310.2 67639 3065.7
## + ethnic_group:wkly_study_hours 8 808.1 68141 3066.0
## + parent_educ:test_prep 5 83.1 68866 3066.3
## - parent_marital_status:wkly_study_hours 6 2636.8 71586 3067.1
## - parent_marital_status:is_first_child 3 2492.4 71441 3071.9
## + ethnic_group:parent_educ 20 2530.7 66418 3074.9
##
## Step: AIC=3054.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 102.1 69414 3051.0
## - is_first_child:wkly_study_hours 2 207.0 69519 3051.8
## - ethnic_group:parent_marital_status 11 2366.0 71678 3051.9
## - transport_means:wkly_study_hours 2 212.7 69525 3051.9
## - gender:transport_means 1 1.3 69313 3052.1
## - gender:test_prep 1 3.7 69316 3052.1
## - ethnic_group:lunch_type 4 722.5 70035 3052.2
## - gender:is_first_child 1 19.3 69331 3052.2
## - gender:lunch_type 1 29.1 69341 3052.3
## - practice_sport:transport_means 2 265.1 69577 3052.3
## - gender:wkly_study_hours 2 288.0 69600 3052.5
## - test_prep:is_first_child 1 76.6 69389 3052.7
## - test_prep:practice_sport 2 327.5 69640 3052.9
## - gender:practice_sport 2 339.9 69652 3053.0
## - lunch_type:test_prep 1 110.6 69423 3053.0
## - lunch_type:is_first_child 1 118.9 69431 3053.1
## - parent_educ:practice_sport 10 2314.2 71626 3053.5
## - ethnic_group:is_first_child 4 882.6 70195 3053.6
## - test_prep:transport_means 1 191.4 69503 3053.7
## <none> 69312 3054.1
## - is_first_child:transport_means 1 236.1 69548 3054.1
## - lunch_type:transport_means 1 283.0 69595 3054.5
## - practice_sport:wkly_study_hours 4 1043.8 70356 3054.9
## - parent_educ:is_first_child 5 1292.5 70605 3055.0
## - ethnic_group:transport_means 4 1109.2 70421 3055.5
## - parent_educ:parent_marital_status 15 3835.0 73147 3055.9
## - parent_marital_status:transport_means 3 935.7 70248 3056.0
## - test_prep:wkly_study_hours 2 703.5 70016 3056.1
## - lunch_type:wkly_study_hours 2 778.6 70091 3056.7
## + lunch_type:parent_marital_status 3 363.1 68949 3057.0
## + test_prep:parent_marital_status 2 100.8 69211 3057.2
## + ethnic_group:test_prep 4 502.5 68810 3057.8
## + parent_educ:transport_means 5 651.6 68660 3058.5
## + parent_marital_status:practice_sport 5 507.8 68804 3059.8
## + gender:parent_marital_status 3 19.6 69293 3059.9
## + gender:parent_educ 5 471.7 68840 3060.1
## + gender:ethnic_group 4 167.2 69145 3060.7
## - lunch_type:practice_sport 2 1267.6 70580 3060.8
## + parent_educ:lunch_type 5 356.7 68955 3061.0
## + ethnic_group:practice_sport 8 1016.1 68296 3061.4
## + parent_educ:wkly_study_hours 10 1340.9 67971 3062.6
## + ethnic_group:wkly_study_hours 8 789.2 68523 3063.3
## - parent_marital_status:wkly_study_hours 6 2550.9 71863 3063.4
## + parent_educ:test_prep 5 50.5 69262 3063.7
## - parent_marital_status:is_first_child 3 2435.5 71748 3068.5
## + ethnic_group:parent_educ 20 2270.2 67042 3074.4
##
## Step: AIC=3050.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 11 2305.2 71719 3048.2
## - is_first_child:wkly_study_hours 2 191.9 69606 3048.6
## - transport_means:wkly_study_hours 2 205.6 69620 3048.7
## - practice_sport:transport_means 2 236.5 69651 3049.0
## - gender:transport_means 1 2.8 69417 3049.0
## - gender:test_prep 1 5.6 69420 3049.0
## - ethnic_group:lunch_type 4 724.5 70139 3049.1
## - gender:is_first_child 1 23.6 69438 3049.2
## - gender:lunch_type 1 38.5 69453 3049.3
## - test_prep:is_first_child 1 52.7 69467 3049.4
## - gender:wkly_study_hours 2 289.2 69703 3049.4
## - gender:practice_sport 2 343.5 69758 3049.9
## - test_prep:practice_sport 2 349.8 69764 3049.9
## - parent_educ:practice_sport 10 2272.3 71686 3050.0
## - lunch_type:test_prep 1 128.0 69542 3050.0
## - lunch_type:is_first_child 1 131.7 69546 3050.1
## - test_prep:transport_means 1 191.5 69606 3050.6
## - ethnic_group:is_first_child 4 907.0 70321 3050.6
## <none> 69414 3051.0
## - lunch_type:transport_means 1 270.0 69684 3051.2
## - is_first_child:transport_means 1 271.7 69686 3051.3
## - parent_educ:is_first_child 5 1261.5 70676 3051.6
## - ethnic_group:transport_means 4 1065.9 70480 3051.9
## - practice_sport:wkly_study_hours 4 1075.9 70490 3052.0
## - parent_educ:parent_marital_status 15 3782.3 73197 3052.3
## - parent_marital_status:transport_means 3 901.5 70316 3052.6
## - test_prep:wkly_study_hours 2 673.0 70087 3052.7
## - lunch_type:wkly_study_hours 2 782.5 70197 3053.6
## + practice_sport:is_first_child 2 102.1 69312 3054.1
## + lunch_type:parent_marital_status 3 336.6 69078 3054.1
## + test_prep:parent_marital_status 2 97.8 69316 3054.1
## + ethnic_group:test_prep 4 524.0 68890 3054.5
## + parent_educ:transport_means 5 604.0 68810 3055.8
## + gender:parent_marital_status 3 18.0 69396 3056.8
## + gender:parent_educ 5 484.2 68930 3056.8
## + parent_marital_status:practice_sport 5 446.7 68968 3057.2
## - lunch_type:practice_sport 2 1235.0 70649 3057.4
## + gender:ethnic_group 4 187.0 69227 3057.4
## + parent_educ:lunch_type 5 356.3 69058 3057.9
## + ethnic_group:practice_sport 8 949.0 68465 3058.8
## + parent_educ:wkly_study_hours 10 1293.2 68121 3059.9
## + ethnic_group:wkly_study_hours 8 799.5 68615 3060.1
## - parent_marital_status:wkly_study_hours 6 2548.9 71963 3060.2
## + parent_educ:test_prep 5 54.2 69360 3060.5
## - parent_marital_status:is_first_child 3 2469.3 71884 3065.6
## + ethnic_group:parent_educ 20 2240.2 67174 3071.6
##
## Step: AIC=3048.23
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 1945.7 73665 3044.0
## - practice_sport:transport_means 2 95.5 71815 3045.0
## - ethnic_group:is_first_child 4 586.8 72306 3045.0
## - transport_means:wkly_study_hours 2 160.4 71880 3045.6
## - is_first_child:wkly_study_hours 2 167.1 71886 3045.6
## - gender:wkly_study_hours 2 199.5 71919 3045.9
## - ethnic_group:lunch_type 4 741.3 72461 3046.3
## - gender:transport_means 1 24.5 71744 3046.4
## - gender:test_prep 1 37.7 71757 3046.5
## - test_prep:is_first_child 1 40.0 71759 3046.6
## - gender:lunch_type 1 42.6 71762 3046.6
## - gender:is_first_child 1 52.0 71771 3046.7
## - test_prep:practice_sport 2 296.9 72016 3046.7
## - gender:practice_sport 2 338.7 72058 3047.0
## - lunch_type:test_prep 1 98.2 71818 3047.0
## - lunch_type:is_first_child 1 98.2 71818 3047.0
## - test_prep:transport_means 1 173.5 71893 3047.7
## - parent_educ:is_first_child 5 1201.7 72921 3048.0
## <none> 71719 3048.2
## - parent_marital_status:transport_means 3 741.3 72461 3048.3
## - practice_sport:wkly_study_hours 4 990.2 72710 3048.3
## - lunch_type:transport_means 1 320.0 72039 3048.9
## - is_first_child:transport_means 1 356.3 72076 3049.2
## - ethnic_group:transport_means 4 1128.0 72847 3049.4
## - lunch_type:wkly_study_hours 2 705.8 72425 3050.0
## - parent_educ:parent_marital_status 15 3998.6 75718 3050.2
## - test_prep:wkly_study_hours 2 820.6 72540 3050.9
## + ethnic_group:parent_marital_status 11 2305.2 69414 3051.0
## + ethnic_group:test_prep 4 586.9 71132 3051.4
## + practice_sport:is_first_child 2 41.3 71678 3051.9
## - parent_marital_status:wkly_study_hours 6 1941.0 73660 3052.0
## + parent_educ:transport_means 5 747.1 70972 3052.1
## + lunch_type:parent_marital_status 3 219.1 71500 3052.4
## + test_prep:parent_marital_status 3 147.7 71572 3053.0
## + gender:parent_marital_status 3 84.7 71635 3053.5
## + gender:parent_educ 5 442.4 71277 3054.6
## - lunch_type:practice_sport 2 1319.4 73039 3055.0
## + gender:ethnic_group 4 146.6 71573 3055.0
## + parent_educ:lunch_type 5 373.5 71346 3055.2
## + parent_marital_status:practice_sport 6 525.2 71194 3055.9
## + parent_educ:wkly_study_hours 10 1465.5 70254 3056.1
## + ethnic_group:practice_sport 8 879.1 70840 3057.0
## + parent_educ:test_prep 5 50.8 71669 3057.8
## + ethnic_group:wkly_study_hours 8 747.7 70972 3058.1
## - parent_marital_status:is_first_child 3 2272.4 73992 3060.6
## + ethnic_group:parent_educ 20 2384.6 69335 3068.3
##
## Step: AIC=3044.03
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 616.0 74281 3040.9
## - practice_sport:transport_means 2 114.9 73780 3040.9
## - transport_means:wkly_study_hours 2 119.6 73785 3041.0
## - is_first_child:wkly_study_hours 2 175.7 73841 3041.4
## - ethnic_group:lunch_type 4 736.1 74401 3041.9
## - gender:wkly_study_hours 2 246.2 73911 3042.0
## - gender:lunch_type 1 26.0 73691 3042.2
## - gender:practice_sport 2 279.5 73945 3042.3
## - test_prep:is_first_child 1 51.2 73716 3042.4
## - gender:transport_means 1 53.1 73718 3042.4
## - gender:test_prep 1 56.7 73722 3042.5
## - gender:is_first_child 1 66.4 73731 3042.6
## - lunch_type:is_first_child 1 79.2 73744 3042.7
## - test_prep:practice_sport 2 349.4 74014 3042.8
## - lunch_type:test_prep 1 121.2 73786 3043.0
## - practice_sport:wkly_study_hours 4 879.5 74545 3043.0
## - test_prep:transport_means 1 145.6 73811 3043.2
## <none> 73665 3044.0
## - is_first_child:transport_means 1 260.1 73925 3044.1
## - lunch_type:transport_means 1 285.2 73950 3044.3
## - parent_educ:is_first_child 5 1425.4 75090 3045.3
## - ethnic_group:transport_means 4 1173.7 74839 3045.3
## - test_prep:wkly_study_hours 2 674.2 74339 3045.4
## - parent_marital_status:transport_means 3 930.7 74596 3045.4
## - lunch_type:wkly_study_hours 2 751.1 74416 3046.0
## + ethnic_group:test_prep 4 596.7 73068 3047.2
## + practice_sport:is_first_child 2 23.4 73642 3047.8
## - parent_educ:parent_marital_status 15 4352.1 78017 3047.9
## - parent_marital_status:wkly_study_hours 6 2020.8 75686 3048.0
## + parent_educ:practice_sport 10 1945.7 71719 3048.2
## + lunch_type:parent_marital_status 3 173.9 73491 3048.6
## + test_prep:parent_marital_status 3 155.5 73510 3048.8
## - lunch_type:practice_sport 2 1103.6 74769 3048.8
## + parent_educ:transport_means 5 643.4 73022 3048.8
## + gender:parent_marital_status 3 77.3 73588 3049.4
## + ethnic_group:parent_marital_status 11 1978.6 71686 3050.0
## + gender:ethnic_group 4 239.4 73426 3050.1
## + gender:parent_educ 5 474.1 73191 3050.2
## + parent_educ:wkly_study_hours 10 1601.0 72064 3051.1
## + parent_educ:lunch_type 5 343.0 73322 3051.3
## + parent_marital_status:practice_sport 6 420.8 73244 3052.6
## + ethnic_group:practice_sport 8 895.6 72769 3052.8
## + parent_educ:test_prep 5 96.6 73568 3053.2
## + ethnic_group:wkly_study_hours 8 768.5 72897 3053.8
## - parent_marital_status:is_first_child 3 2307.1 75972 3056.2
## + ethnic_group:parent_educ 20 2365.9 71299 3064.8
##
## Step: AIC=3040.94
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 559.7 74841 3037.4
## - practice_sport:transport_means 2 104.8 74386 3037.8
## - transport_means:wkly_study_hours 2 126.4 74407 3037.9
## - gender:wkly_study_hours 2 196.4 74477 3038.5
## - is_first_child:wkly_study_hours 2 229.6 74511 3038.8
## - gender:practice_sport 2 251.9 74533 3038.9
## - gender:lunch_type 1 14.3 74295 3039.1
## - gender:is_first_child 1 30.8 74312 3039.2
## - gender:test_prep 1 40.0 74321 3039.3
## - gender:transport_means 1 58.5 74340 3039.4
## - test_prep:is_first_child 1 75.8 74357 3039.5
## - test_prep:practice_sport 2 350.0 74631 3039.7
## - test_prep:transport_means 1 115.1 74396 3039.8
## - lunch_type:is_first_child 1 119.2 74400 3039.9
## - practice_sport:wkly_study_hours 4 880.0 75161 3039.9
## - is_first_child:transport_means 1 144.6 74426 3040.1
## - lunch_type:test_prep 1 149.4 74430 3040.1
## <none> 74281 3040.9
## - lunch_type:transport_means 1 261.8 74543 3041.0
## - test_prep:wkly_study_hours 2 522.3 74803 3041.1
## - parent_marital_status:transport_means 3 939.6 75221 3042.3
## - lunch_type:wkly_study_hours 2 692.9 74974 3042.4
## - parent_educ:is_first_child 5 1465.0 75746 3042.5
## - ethnic_group:transport_means 4 1307.4 75588 3043.2
## - parent_educ:parent_marital_status 15 4239.6 78521 3043.7
## + ethnic_group:is_first_child 4 616.0 73665 3044.0
## + ethnic_group:test_prep 4 581.5 73700 3044.3
## - parent_marital_status:wkly_study_hours 6 1978.0 76259 3044.4
## + practice_sport:is_first_child 2 40.8 74240 3044.6
## + parent_educ:practice_sport 10 1974.9 72306 3045.0
## + test_prep:parent_marital_status 3 184.2 74097 3045.5
## - lunch_type:practice_sport 2 1103.4 75384 3045.6
## + lunch_type:parent_marital_status 3 140.1 74141 3045.8
## + parent_educ:transport_means 5 610.0 73671 3046.1
## + gender:parent_marital_status 3 67.0 74214 3046.4
## + gender:ethnic_group 4 192.3 74089 3047.4
## + gender:parent_educ 5 422.0 73859 3047.6
## + parent_educ:wkly_study_hours 10 1654.5 72627 3047.7
## + parent_educ:lunch_type 5 349.3 73932 3048.2
## + ethnic_group:parent_marital_status 11 1673.1 72608 3049.5
## + parent_marital_status:practice_sport 6 385.1 73896 3049.9
## + parent_educ:test_prep 5 113.8 74167 3050.0
## + ethnic_group:practice_sport 8 857.0 73424 3050.1
## + ethnic_group:wkly_study_hours 8 741.7 73539 3051.0
## - parent_marital_status:is_first_child 3 2299.8 76581 3052.9
## + ethnic_group:parent_educ 20 2402.3 71879 3061.5
##
## Step: AIC=3037.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 90.2 74931 3034.1
## - transport_means:wkly_study_hours 2 140.4 74981 3034.5
## - gender:wkly_study_hours 2 204.9 75046 3035.0
## - gender:practice_sport 2 215.5 75056 3035.1
## - is_first_child:wkly_study_hours 2 223.2 75064 3035.1
## - gender:lunch_type 1 15.2 74856 3035.5
## - practice_sport:wkly_study_hours 4 784.5 75625 3035.5
## - gender:is_first_child 1 33.8 74875 3035.6
## - gender:test_prep 1 48.7 74889 3035.8
## - gender:transport_means 1 52.5 74893 3035.8
## - test_prep:is_first_child 1 66.9 74908 3035.9
## - lunch_type:is_first_child 1 106.1 74947 3036.2
## - test_prep:transport_means 1 128.1 74969 3036.4
## - is_first_child:transport_means 1 137.8 74979 3036.4
## - test_prep:practice_sport 2 407.4 75248 3036.6
## - lunch_type:test_prep 1 182.2 75023 3036.8
## <none> 74841 3037.4
## - test_prep:wkly_study_hours 2 520.3 75361 3037.5
## - lunch_type:transport_means 1 325.7 75166 3037.9
## - parent_educ:parent_marital_status 15 4029.3 78870 3038.3
## - lunch_type:wkly_study_hours 2 641.3 75482 3038.4
## - parent_marital_status:transport_means 3 902.6 75743 3038.4
## - ethnic_group:transport_means 4 1226.6 76067 3039.0
## - parent_educ:is_first_child 5 1535.8 76377 3039.3
## + ethnic_group:lunch_type 4 559.7 74281 3040.9
## + practice_sport:is_first_child 2 47.5 74793 3041.0
## - parent_marital_status:wkly_study_hours 6 2059.5 76900 3041.4
## + ethnic_group:test_prep 4 468.2 74373 3041.7
## + parent_educ:practice_sport 10 1964.0 72877 3041.7
## + test_prep:parent_marital_status 3 192.8 74648 3041.8
## + ethnic_group:is_first_child 4 439.7 74401 3041.9
## + parent_educ:transport_means 5 683.2 74158 3042.0
## + lunch_type:parent_marital_status 3 164.7 74676 3042.1
## + gender:parent_marital_status 3 61.4 74779 3042.9
## - lunch_type:practice_sport 2 1228.5 76069 3043.0
## + gender:ethnic_group 4 211.7 74629 3043.7
## + parent_educ:lunch_type 5 391.3 74449 3044.3
## + gender:parent_educ 5 376.2 74465 3044.4
## + parent_marital_status:practice_sport 6 466.6 74374 3045.7
## + ethnic_group:practice_sport 8 965.1 73876 3045.7
## + ethnic_group:parent_marital_status 11 1696.6 73144 3045.8
## + parent_educ:wkly_study_hours 10 1444.5 73396 3045.9
## + parent_educ:test_prep 5 122.2 74719 3046.4
## + ethnic_group:wkly_study_hours 8 794.9 74046 3047.1
## - parent_marital_status:is_first_child 3 2267.8 77109 3049.0
## + ethnic_group:parent_educ 20 2517.8 72323 3057.2
##
## Step: AIC=3034.08
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 152.6 75084 3031.3
## - gender:practice_sport 2 202.8 75134 3031.7
## - gender:wkly_study_hours 2 209.1 75140 3031.7
## - is_first_child:wkly_study_hours 2 215.6 75147 3031.8
## - practice_sport:wkly_study_hours 4 763.7 75695 3032.1
## - gender:lunch_type 1 15.9 74947 3032.2
## - gender:is_first_child 1 39.1 74970 3032.4
## - gender:test_prep 1 46.4 74977 3032.4
## - gender:transport_means 1 52.6 74984 3032.5
## - test_prep:is_first_child 1 65.8 74997 3032.6
## - lunch_type:is_first_child 1 113.8 75045 3033.0
## - test_prep:transport_means 1 124.1 75055 3033.1
## - test_prep:practice_sport 2 399.1 75330 3033.2
## - is_first_child:transport_means 1 157.6 75089 3033.3
## - lunch_type:test_prep 1 200.4 75131 3033.7
## <none> 74931 3034.1
## - test_prep:wkly_study_hours 2 521.1 75452 3034.2
## - lunch_type:transport_means 1 334.9 75266 3034.7
## - parent_educ:parent_marital_status 15 4028.6 78960 3035.0
## - lunch_type:wkly_study_hours 2 635.2 75566 3035.1
## - parent_marital_status:transport_means 3 917.6 75849 3035.3
## - ethnic_group:transport_means 4 1237.8 76169 3035.8
## - parent_educ:is_first_child 5 1530.9 76462 3036.0
## + practice_sport:transport_means 2 90.2 74841 3037.4
## + ethnic_group:lunch_type 4 545.2 74386 3037.8
## + practice_sport:is_first_child 2 36.5 74894 3037.8
## - parent_marital_status:wkly_study_hours 6 2071.5 77003 3038.2
## + parent_educ:practice_sport 10 1980.6 72950 3038.3
## + ethnic_group:test_prep 4 468.3 74463 3038.4
## + test_prep:parent_marital_status 3 193.8 74737 3038.6
## + ethnic_group:is_first_child 4 436.2 74495 3038.6
## + lunch_type:parent_marital_status 3 164.8 74766 3038.8
## + parent_educ:transport_means 5 623.6 74307 3039.2
## - lunch_type:practice_sport 2 1207.3 76138 3039.5
## + gender:parent_marital_status 3 49.0 74882 3039.7
## + gender:ethnic_group 4 211.2 74720 3040.4
## + parent_educ:lunch_type 5 407.0 74524 3040.9
## + gender:parent_educ 5 361.2 74570 3041.2
## + parent_marital_status:practice_sport 6 464.0 74467 3042.4
## + ethnic_group:practice_sport 8 951.2 73980 3042.5
## + parent_educ:test_prep 5 126.5 74805 3043.1
## + ethnic_group:parent_marital_status 11 1608.8 73322 3043.3
## + parent_educ:wkly_study_hours 10 1355.5 73576 3043.3
## + ethnic_group:wkly_study_hours 8 794.8 74136 3043.8
## - parent_marital_status:is_first_child 3 2227.1 77158 3045.4
## + ethnic_group:parent_educ 20 2387.1 72544 3055.0
##
## Step: AIC=3031.28
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 200.3 75284 3028.8
## - gender:practice_sport 2 213.6 75297 3029.0
## - is_first_child:wkly_study_hours 2 235.6 75319 3029.1
## - practice_sport:wkly_study_hours 4 769.9 75854 3029.3
## - gender:lunch_type 1 13.4 75097 3029.4
## - gender:is_first_child 1 36.5 75120 3029.6
## - gender:test_prep 1 36.9 75121 3029.6
## - gender:transport_means 1 52.0 75136 3029.7
## - test_prep:is_first_child 1 73.0 75157 3029.8
## - test_prep:transport_means 1 106.3 75190 3030.1
## - lunch_type:is_first_child 1 117.0 75201 3030.2
## - is_first_child:transport_means 1 155.5 75239 3030.5
## - test_prep:practice_sport 2 432.0 75516 3030.7
## - lunch_type:test_prep 1 202.7 75286 3030.9
## - test_prep:wkly_study_hours 2 502.3 75586 3031.2
## <none> 75084 3031.3
## - lunch_type:transport_means 1 316.8 75400 3031.8
## - parent_educ:parent_marital_status 15 4009.8 79093 3032.0
## - parent_marital_status:transport_means 3 899.1 75983 3032.3
## - lunch_type:wkly_study_hours 2 642.7 75726 3032.3
## - parent_educ:is_first_child 5 1516.3 76600 3033.1
## - ethnic_group:transport_means 4 1313.2 76397 3033.5
## + transport_means:wkly_study_hours 2 152.6 74931 3034.1
## + practice_sport:transport_means 2 102.4 74981 3034.5
## + ethnic_group:lunch_type 4 557.6 74526 3034.9
## + practice_sport:is_first_child 2 38.3 75045 3035.0
## + ethnic_group:test_prep 4 478.7 74605 3035.5
## - parent_marital_status:wkly_study_hours 6 2093.8 77177 3035.5
## + test_prep:parent_marital_status 3 190.2 74893 3035.8
## + ethnic_group:is_first_child 4 437.3 74646 3035.8
## + parent_educ:practice_sport 10 1938.5 73145 3035.8
## + lunch_type:parent_marital_status 3 176.1 74908 3035.9
## + parent_educ:transport_means 5 615.5 74468 3036.4
## - lunch_type:practice_sport 2 1206.4 76290 3036.7
## + gender:parent_marital_status 3 42.7 75041 3036.9
## + gender:ethnic_group 4 235.5 74848 3037.4
## + parent_educ:lunch_type 5 412.6 74671 3038.0
## + gender:parent_educ 5 381.1 74703 3038.3
## + ethnic_group:practice_sport 8 981.1 74103 3039.5
## + parent_marital_status:practice_sport 6 470.9 74613 3039.6
## + parent_educ:test_prep 5 132.3 74951 3040.2
## + parent_educ:wkly_study_hours 10 1382.8 73701 3040.3
## + ethnic_group:parent_marital_status 11 1599.1 73485 3040.6
## + ethnic_group:wkly_study_hours 8 685.4 74398 3041.9
## - parent_marital_status:is_first_child 3 2151.3 77235 3041.9
## + ethnic_group:parent_educ 20 2409.9 72674 3052.0
##
## Step: AIC=3028.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 224.7 75509 3026.6
## - gender:practice_sport 2 227.7 75512 3026.6
## - practice_sport:wkly_study_hours 4 746.4 76030 3026.7
## - gender:lunch_type 1 9.6 75293 3026.9
## - gender:is_first_child 1 35.4 75319 3027.1
## - gender:test_prep 1 54.5 75338 3027.3
## - gender:transport_means 1 55.2 75339 3027.3
## - test_prep:is_first_child 1 91.8 75376 3027.6
## - lunch_type:is_first_child 1 110.5 75394 3027.7
## - test_prep:transport_means 1 115.1 75399 3027.8
## - is_first_child:transport_means 1 143.5 75427 3028.0
## - test_prep:practice_sport 2 412.6 75696 3028.1
## - lunch_type:test_prep 1 200.7 75485 3028.4
## - test_prep:wkly_study_hours 2 501.3 75785 3028.8
## <none> 75284 3028.8
## - lunch_type:transport_means 1 311.9 75596 3029.3
## - lunch_type:wkly_study_hours 2 588.5 75872 3029.4
## - parent_educ:parent_marital_status 15 4077.9 79362 3030.0
## - parent_marital_status:transport_means 3 918.3 76202 3030.0
## - parent_educ:is_first_child 5 1504.4 76788 3030.5
## - ethnic_group:transport_means 4 1307.8 76592 3031.0
## + gender:wkly_study_hours 2 200.3 75084 3031.3
## + transport_means:wkly_study_hours 2 143.7 75140 3031.7
## + practice_sport:transport_means 2 106.7 75177 3032.0
## + ethnic_group:lunch_type 4 564.3 74720 3032.4
## + practice_sport:is_first_child 2 35.0 75249 3032.6
## + ethnic_group:test_prep 4 500.5 74783 3032.9
## + parent_educ:practice_sport 10 1975.2 73309 3033.2
## + test_prep:parent_marital_status 3 190.2 75094 3033.4
## + lunch_type:parent_marital_status 3 151.8 75132 3033.7
## + ethnic_group:is_first_child 4 393.3 74891 3033.8
## - lunch_type:practice_sport 2 1171.7 76456 3034.0
## + parent_educ:transport_means 5 584.3 74700 3034.2
## + gender:parent_marital_status 3 40.2 75244 3034.5
## - parent_marital_status:wkly_study_hours 6 2307.6 77592 3034.7
## + gender:ethnic_group 4 245.5 75038 3034.9
## + gender:parent_educ 5 409.5 74874 3035.6
## + parent_educ:lunch_type 5 400.9 74883 3035.7
## + ethnic_group:practice_sport 8 1028.4 74255 3036.7
## + parent_marital_status:practice_sport 6 482.3 74802 3037.1
## + parent_educ:wkly_study_hours 10 1462.3 73822 3037.3
## + parent_educ:test_prep 5 144.3 75140 3037.7
## + ethnic_group:parent_marital_status 11 1560.9 73723 3038.5
## - parent_marital_status:is_first_child 3 2096.8 77381 3039.1
## + ethnic_group:wkly_study_hours 8 665.0 74619 3039.6
## + ethnic_group:parent_educ 20 2348.0 72936 3050.2
##
## Step: AIC=3026.61
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 221.8 75730 3024.3
## - gender:lunch_type 1 8.1 75517 3024.7
## - practice_sport:wkly_study_hours 4 815.9 76325 3024.9
## - gender:is_first_child 1 47.0 75556 3025.0
## - gender:test_prep 1 56.0 75565 3025.1
## - gender:transport_means 1 60.8 75569 3025.1
## - test_prep:is_first_child 1 66.3 75575 3025.1
## - is_first_child:transport_means 1 121.9 75631 3025.6
## - test_prep:practice_sport 2 387.2 75896 3025.6
## - test_prep:transport_means 1 132.1 75641 3025.6
## - lunch_type:is_first_child 1 147.3 75656 3025.8
## - lunch_type:test_prep 1 226.8 75735 3026.4
## - test_prep:wkly_study_hours 2 504.9 76014 3026.5
## <none> 75509 3026.6
## - lunch_type:transport_means 1 315.6 75824 3027.1
## - parent_marital_status:transport_means 3 854.9 76364 3027.2
## - lunch_type:wkly_study_hours 2 599.4 76108 3027.3
## - parent_educ:is_first_child 5 1416.9 76926 3027.6
## - parent_educ:parent_marital_status 15 4118.0 79627 3027.9
## - ethnic_group:transport_means 4 1292.0 76801 3028.6
## + is_first_child:wkly_study_hours 2 224.7 75284 3028.8
## + gender:wkly_study_hours 2 189.4 75319 3029.1
## + transport_means:wkly_study_hours 2 162.2 75346 3029.3
## + practice_sport:transport_means 2 99.0 75410 3029.8
## + ethnic_group:lunch_type 4 561.9 74947 3030.2
## + practice_sport:is_first_child 2 29.1 75480 3030.4
## + ethnic_group:test_prep 4 516.9 74992 3030.6
## + test_prep:parent_marital_status 3 216.2 75292 3030.9
## + parent_educ:practice_sport 10 1970.1 73539 3031.0
## + ethnic_group:is_first_child 4 436.1 75073 3031.2
## + lunch_type:parent_marital_status 3 148.9 75360 3031.4
## + parent_educ:transport_means 5 557.1 74952 3032.2
## + gender:parent_marital_status 3 43.2 75466 3032.3
## + gender:ethnic_group 4 258.6 75250 3032.6
## - lunch_type:practice_sport 2 1314.3 76823 3032.8
## - parent_marital_status:wkly_study_hours 6 2397.4 77906 3033.1
## + gender:parent_educ 5 449.5 75059 3033.1
## + parent_educ:lunch_type 5 402.2 75106 3033.5
## + ethnic_group:practice_sport 8 1054.8 74454 3034.3
## + parent_marital_status:practice_sport 6 535.4 74973 3034.4
## + parent_educ:wkly_study_hours 10 1496.8 74012 3034.8
## + parent_educ:test_prep 5 130.5 75378 3035.6
## - parent_marital_status:is_first_child 3 2033.1 77542 3036.3
## + ethnic_group:parent_marital_status 11 1481.0 74028 3036.9
## + ethnic_group:wkly_study_hours 8 699.9 74809 3037.1
## + ethnic_group:parent_educ 20 2251.9 73257 3048.8
##
## Step: AIC=3024.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:is_first_child + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 8.4 75739 3022.4
## - test_prep:is_first_child 1 55.9 75786 3022.8
## - gender:is_first_child 1 57.4 75788 3022.8
## - gender:transport_means 1 71.5 75802 3022.9
## - gender:test_prep 1 71.6 75802 3022.9
## - practice_sport:wkly_study_hours 4 886.4 76617 3023.2
## - test_prep:transport_means 1 123.7 75854 3023.3
## - is_first_child:transport_means 1 137.4 75868 3023.4
## - test_prep:practice_sport 2 423.8 76154 3023.6
## - lunch_type:is_first_child 1 180.2 75911 3023.7
## - lunch_type:test_prep 1 217.8 75948 3024.0
## - test_prep:wkly_study_hours 2 495.1 76226 3024.2
## <none> 75730 3024.3
## - parent_marital_status:transport_means 3 814.9 76545 3024.7
## - lunch_type:wkly_study_hours 2 575.3 76306 3024.8
## - lunch_type:transport_means 1 337.3 76068 3025.0
## - parent_educ:is_first_child 5 1435.2 77166 3025.4
## - parent_educ:parent_marital_status 15 4197.3 79928 3026.2
## - ethnic_group:transport_means 4 1300.0 77030 3026.4
## + gender:practice_sport 2 221.8 75509 3026.6
## + is_first_child:wkly_study_hours 2 218.8 75512 3026.6
## + gender:wkly_study_hours 2 202.8 75528 3026.8
## + transport_means:wkly_study_hours 2 172.4 75558 3027.0
## + practice_sport:transport_means 2 85.5 75645 3027.7
## + practice_sport:is_first_child 2 28.3 75702 3028.1
## + ethnic_group:lunch_type 4 527.5 75203 3028.2
## + ethnic_group:test_prep 4 516.9 75214 3028.3
## + test_prep:parent_marital_status 3 200.8 75530 3028.8
## + ethnic_group:is_first_child 4 413.3 75317 3029.1
## + parent_educ:practice_sport 10 1917.0 73813 3029.2
## + lunch_type:parent_marital_status 3 137.0 75593 3029.3
## + parent_educ:transport_means 5 565.9 75165 3029.9
## + gender:parent_marital_status 3 52.3 75678 3029.9
## - parent_marital_status:wkly_study_hours 6 2321.3 78052 3030.2
## + gender:ethnic_group 4 216.3 75514 3030.7
## - lunch_type:practice_sport 2 1351.3 77082 3030.8
## + gender:parent_educ 5 453.1 75277 3030.8
## + parent_educ:lunch_type 5 416.7 75314 3031.1
## + ethnic_group:practice_sport 8 1124.5 74606 3031.5
## + parent_marital_status:practice_sport 6 558.5 75172 3032.0
## + parent_educ:wkly_study_hours 10 1460.2 74270 3032.8
## + parent_educ:test_prep 5 130.2 75600 3033.3
## - parent_marital_status:is_first_child 3 2060.2 77791 3034.2
## + ethnic_group:parent_marital_status 11 1515.3 74215 3034.4
## + ethnic_group:wkly_study_hours 8 702.9 75028 3034.8
## + ethnic_group:parent_educ 20 2304.5 73426 3046.1
##
## Step: AIC=3022.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:is_first_child +
## gender:transport_means + ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 57.0 75796 3020.8
## - test_prep:is_first_child 1 57.1 75796 3020.8
## - gender:test_prep 1 69.1 75808 3020.9
## - gender:transport_means 1 72.9 75812 3021.0
## - practice_sport:wkly_study_hours 4 884.1 76623 3021.2
## - test_prep:transport_means 1 127.3 75866 3021.4
## - is_first_child:transport_means 1 134.3 75873 3021.4
## - test_prep:practice_sport 2 429.7 76169 3021.7
## - lunch_type:is_first_child 1 182.4 75921 3021.8
## - lunch_type:test_prep 1 226.2 75965 3022.2
## - test_prep:wkly_study_hours 2 500.1 76239 3022.3
## <none> 75739 3022.4
## - parent_marital_status:transport_means 3 808.4 76547 3022.7
## - lunch_type:wkly_study_hours 2 572.3 76311 3022.8
## - lunch_type:transport_means 1 345.8 76085 3023.1
## - parent_educ:is_first_child 5 1434.6 77173 3023.5
## - parent_educ:parent_marital_status 15 4194.5 79933 3024.2
## + gender:lunch_type 1 8.4 75730 3024.3
## - ethnic_group:transport_means 4 1313.0 77052 3024.6
## + gender:practice_sport 2 222.1 75517 3024.7
## + is_first_child:wkly_study_hours 2 217.1 75522 3024.7
## + gender:wkly_study_hours 2 199.5 75539 3024.8
## + transport_means:wkly_study_hours 2 170.3 75569 3025.1
## + practice_sport:transport_means 2 85.8 75653 3025.7
## + practice_sport:is_first_child 2 28.3 75711 3026.2
## + ethnic_group:lunch_type 4 527.2 75212 3026.3
## + ethnic_group:test_prep 4 519.0 75220 3026.3
## + test_prep:parent_marital_status 3 203.5 75535 3026.8
## + ethnic_group:is_first_child 4 409.1 75330 3027.2
## + lunch_type:parent_marital_status 3 142.1 75597 3027.3
## + parent_educ:practice_sport 10 1903.8 73835 3027.4
## + parent_educ:transport_means 5 572.4 75166 3027.9
## + gender:parent_marital_status 3 51.1 75688 3028.0
## - parent_marital_status:wkly_study_hours 6 2359.0 78098 3028.5
## + gender:ethnic_group 4 216.1 75523 3028.7
## + gender:parent_educ 5 450.2 75289 3028.9
## + parent_educ:lunch_type 5 424.1 75315 3029.1
## - lunch_type:practice_sport 2 1386.6 77125 3029.1
## + ethnic_group:practice_sport 8 1102.7 74636 3029.8
## + parent_marital_status:practice_sport 6 554.6 75184 3030.1
## + parent_educ:wkly_study_hours 10 1456.2 74283 3030.9
## + parent_educ:test_prep 5 128.7 75610 3031.4
## - parent_marital_status:is_first_child 3 2051.8 77791 3032.2
## + ethnic_group:parent_marital_status 11 1513.5 74225 3032.5
## + ethnic_group:wkly_study_hours 8 705.0 75034 3032.9
## + ethnic_group:parent_educ 20 2265.2 73474 3044.5
##
## Step: AIC=3020.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 63.1 75859 3019.3
## - test_prep:is_first_child 1 65.8 75862 3019.4
## - gender:transport_means 1 71.8 75868 3019.4
## - is_first_child:transport_means 1 124.6 75921 3019.8
## - test_prep:transport_means 1 129.3 75925 3019.8
## - practice_sport:wkly_study_hours 4 920.1 76716 3020.0
## - test_prep:practice_sport 2 414.2 76210 3020.1
## - lunch_type:is_first_child 1 171.5 75967 3020.2
## - test_prep:wkly_study_hours 2 490.6 76286 3020.7
## - lunch_type:test_prep 1 235.7 76032 3020.7
## <none> 75796 3020.8
## - lunch_type:wkly_study_hours 2 573.9 76370 3021.3
## - parent_marital_status:transport_means 3 837.6 76634 3021.3
## - lunch_type:transport_means 1 365.6 76161 3021.7
## - parent_educ:is_first_child 5 1471.7 77268 3022.2
## + gender:is_first_child 1 57.0 75739 3022.4
## - parent_educ:parent_marital_status 15 4190.6 79986 3022.6
## + gender:lunch_type 1 8.1 75788 3022.8
## + gender:practice_sport 2 232.2 75564 3023.0
## + is_first_child:wkly_study_hours 2 230.4 75565 3023.1
## + gender:wkly_study_hours 2 198.3 75598 3023.3
## - ethnic_group:transport_means 4 1355.1 77151 3023.3
## + transport_means:wkly_study_hours 2 165.8 75630 3023.6
## + practice_sport:transport_means 2 91.4 75704 3024.1
## + practice_sport:is_first_child 2 30.8 75765 3024.6
## + ethnic_group:lunch_type 4 528.1 75268 3024.7
## + ethnic_group:test_prep 4 488.7 75307 3025.0
## + test_prep:parent_marital_status 3 207.7 75588 3025.2
## + lunch_type:parent_marital_status 3 150.2 75646 3025.7
## + parent_educ:practice_sport 10 1908.4 73887 3025.8
## + ethnic_group:is_first_child 4 370.0 75426 3026.0
## + gender:parent_marital_status 3 58.6 75737 3026.4
## + parent_educ:transport_means 5 568.5 75227 3026.4
## - parent_marital_status:wkly_study_hours 6 2312.6 78108 3026.6
## + gender:ethnic_group 4 219.5 75576 3027.1
## + parent_educ:lunch_type 5 453.2 75343 3027.3
## + gender:parent_educ 5 447.8 75348 3027.3
## - lunch_type:practice_sport 2 1433.9 77230 3027.9
## + ethnic_group:practice_sport 8 1075.1 74721 3028.4
## + parent_marital_status:practice_sport 6 536.8 75259 3028.7
## + parent_educ:wkly_study_hours 10 1464.0 74332 3029.3
## + parent_educ:test_prep 5 129.7 75666 3029.8
## - parent_marital_status:is_first_child 3 2041.9 77838 3030.5
## + ethnic_group:parent_marital_status 11 1532.8 74263 3030.8
## + ethnic_group:wkly_study_hours 8 698.7 75097 3031.4
## + ethnic_group:parent_educ 20 2190.8 73605 3043.5
##
## Step: AIC=3019.34
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:transport_means +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 61.1 75920 3017.8
## - test_prep:is_first_child 1 66.6 75926 3017.9
## - is_first_child:transport_means 1 121.1 75980 3018.3
## - test_prep:transport_means 1 123.3 75982 3018.3
## - practice_sport:wkly_study_hours 4 907.1 76766 3018.3
## - test_prep:practice_sport 2 408.5 76267 3018.5
## - lunch_type:is_first_child 1 162.8 76022 3018.6
## - test_prep:wkly_study_hours 2 472.7 76332 3019.0
## - lunch_type:test_prep 1 249.1 76108 3019.3
## <none> 75859 3019.3
## - lunch_type:wkly_study_hours 2 582.1 76441 3019.8
## - parent_marital_status:transport_means 3 852.8 76712 3019.9
## - lunch_type:transport_means 1 379.7 76239 3020.3
## - parent_educ:is_first_child 5 1449.5 77308 3020.5
## - parent_educ:parent_marital_status 15 4159.3 80018 3020.8
## + gender:test_prep 1 63.1 75796 3020.8
## + gender:is_first_child 1 51.0 75808 3020.9
## + gender:lunch_type 1 5.8 75853 3021.3
## + gender:practice_sport 2 246.4 75613 3021.4
## + is_first_child:wkly_study_hours 2 231.2 75628 3021.5
## + gender:wkly_study_hours 2 218.9 75640 3021.6
## - ethnic_group:transport_means 4 1372.6 77232 3021.9
## + transport_means:wkly_study_hours 2 153.6 75705 3022.1
## + practice_sport:transport_means 2 88.4 75771 3022.7
## + practice_sport:is_first_child 2 33.0 75826 3023.1
## + ethnic_group:lunch_type 4 538.8 75320 3023.1
## + ethnic_group:test_prep 4 464.8 75394 3023.7
## + test_prep:parent_marital_status 3 205.5 75653 3023.7
## + lunch_type:parent_marital_status 3 157.5 75702 3024.1
## + parent_educ:practice_sport 10 1925.9 73933 3024.2
## + ethnic_group:is_first_child 4 351.2 75508 3024.6
## - parent_marital_status:wkly_study_hours 6 2281.3 78140 3024.8
## + gender:parent_marital_status 3 61.3 75798 3024.9
## + parent_educ:transport_means 5 558.7 75300 3025.0
## + gender:ethnic_group 4 231.9 75627 3025.5
## + gender:parent_educ 5 446.9 75412 3025.8
## + parent_educ:lunch_type 5 444.2 75415 3025.9
## - lunch_type:practice_sport 2 1417.7 77277 3026.3
## + parent_marital_status:practice_sport 6 550.5 75308 3027.0
## + ethnic_group:practice_sport 8 1054.5 74804 3027.1
## + parent_educ:wkly_study_hours 10 1478.9 74380 3027.7
## + parent_educ:test_prep 5 132.2 75727 3028.3
## - parent_marital_status:is_first_child 3 2002.0 77861 3028.7
## + ethnic_group:parent_marital_status 11 1567.5 74291 3029.0
## + ethnic_group:wkly_study_hours 8 725.0 75134 3029.7
## + ethnic_group:parent_educ 20 2197.5 73662 3042.0
##
## Step: AIC=3017.81
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 71.6 75992 3016.4
## - practice_sport:wkly_study_hours 4 888.2 76808 3016.7
## - is_first_child:transport_means 1 131.9 76052 3016.8
## - test_prep:transport_means 1 138.8 76059 3016.9
## - test_prep:practice_sport 2 403.4 76323 3016.9
## - lunch_type:is_first_child 1 150.7 76071 3017.0
## - test_prep:wkly_study_hours 2 477.5 76397 3017.5
## - lunch_type:test_prep 1 253.8 76174 3017.8
## <none> 75920 3017.8
## - lunch_type:wkly_study_hours 2 565.9 76486 3018.2
## - parent_marital_status:transport_means 3 851.0 76771 3018.4
## - parent_educ:is_first_child 5 1432.0 77352 3018.8
## - lunch_type:transport_means 1 393.6 76314 3018.9
## - parent_educ:parent_marital_status 15 4127.3 80047 3019.1
## + gender:transport_means 1 61.1 75859 3019.3
## + gender:test_prep 1 52.4 75868 3019.4
## + gender:is_first_child 1 50.5 75870 3019.4
## + gender:lunch_type 1 7.1 75913 3019.8
## + gender:practice_sport 2 255.3 75665 3019.8
## + is_first_child:wkly_study_hours 2 236.9 75683 3020.0
## + gender:wkly_study_hours 2 221.6 75698 3020.1
## - ethnic_group:transport_means 4 1335.2 77255 3020.1
## + transport_means:wkly_study_hours 2 154.0 75766 3020.6
## + practice_sport:transport_means 2 89.3 75831 3021.1
## + practice_sport:is_first_child 2 37.7 75882 3021.5
## + ethnic_group:lunch_type 4 532.3 75388 3021.7
## + ethnic_group:test_prep 4 467.3 75453 3022.2
## + test_prep:parent_marital_status 3 200.6 75719 3022.2
## + parent_educ:practice_sport 10 1954.7 73965 3022.4
## + lunch_type:parent_marital_status 3 160.5 75760 3022.6
## + ethnic_group:is_first_child 4 355.2 75565 3023.1
## - parent_marital_status:wkly_study_hours 6 2270.6 78191 3023.2
## + gender:parent_marital_status 3 59.3 75861 3023.3
## + parent_educ:transport_means 5 560.2 75360 3023.4
## + gender:ethnic_group 4 247.9 75672 3023.9
## + gender:parent_educ 5 449.9 75470 3024.3
## + parent_educ:lunch_type 5 448.9 75471 3024.3
## - lunch_type:practice_sport 2 1396.7 77317 3024.6
## + parent_marital_status:practice_sport 6 550.3 75370 3025.5
## + ethnic_group:practice_sport 8 1036.1 74884 3025.7
## + parent_educ:wkly_study_hours 10 1435.0 74485 3026.6
## + parent_educ:test_prep 5 128.0 75792 3026.8
## + ethnic_group:parent_marital_status 11 1602.7 74317 3027.2
## - parent_marital_status:is_first_child 3 2036.3 77956 3027.4
## + ethnic_group:wkly_study_hours 8 718.1 75202 3028.2
## + ethnic_group:parent_educ 20 2173.1 73747 3040.7
## - gender 1 12750.1 88670 3107.4
##
## Step: AIC=3016.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 915.5 76907 3015.4
## - is_first_child:transport_means 1 140.3 76132 3015.5
## - test_prep:transport_means 1 140.4 76132 3015.5
## - test_prep:practice_sport 2 403.2 76395 3015.5
## - lunch_type:is_first_child 1 166.0 76158 3015.7
## - test_prep:wkly_study_hours 2 471.7 76463 3016.0
## - lunch_type:test_prep 1 244.8 76236 3016.3
## <none> 75992 3016.4
## - parent_marital_status:transport_means 3 837.7 76829 3016.8
## - lunch_type:wkly_study_hours 2 582.5 76574 3016.9
## - parent_educ:is_first_child 5 1386.8 77378 3017.0
## - parent_educ:parent_marital_status 15 4132.9 80125 3017.6
## - lunch_type:transport_means 1 429.9 76421 3017.7
## + test_prep:is_first_child 1 71.6 75920 3017.8
## + gender:transport_means 1 66.1 75926 3017.9
## + gender:is_first_child 1 59.1 75933 3017.9
## + gender:test_prep 1 52.7 75939 3018.0
## + gender:lunch_type 1 8.3 75983 3018.3
## + gender:practice_sport 2 244.1 75748 3018.5
## + gender:wkly_study_hours 2 240.2 75751 3018.5
## - ethnic_group:transport_means 4 1326.3 77318 3018.6
## + is_first_child:wkly_study_hours 2 213.2 75778 3018.7
## + transport_means:wkly_study_hours 2 158.8 75833 3019.1
## + practice_sport:transport_means 2 91.2 75900 3019.7
## + practice_sport:is_first_child 2 28.3 75963 3020.2
## + ethnic_group:lunch_type 4 528.2 75463 3020.3
## + test_prep:parent_marital_status 3 219.9 75772 3020.7
## + ethnic_group:test_prep 4 467.8 75524 3020.7
## + parent_educ:practice_sport 10 1968.3 74023 3020.9
## + lunch_type:parent_marital_status 3 163.3 75828 3021.1
## + ethnic_group:is_first_child 4 365.5 75626 3021.5
## - parent_marital_status:wkly_study_hours 6 2263.7 78255 3021.7
## + parent_educ:transport_means 5 583.3 75408 3021.8
## + gender:parent_marital_status 3 64.3 75927 3021.9
## + gender:ethnic_group 4 233.9 75758 3022.6
## + gender:parent_educ 5 453.0 75539 3022.8
## + parent_educ:lunch_type 5 439.7 75552 3022.9
## - lunch_type:practice_sport 2 1447.7 77439 3023.5
## + parent_marital_status:practice_sport 6 544.3 75447 3024.1
## + ethnic_group:practice_sport 8 1040.0 74952 3024.2
## + parent_educ:wkly_study_hours 10 1447.2 74544 3025.0
## + parent_educ:test_prep 5 136.2 75855 3025.3
## - parent_marital_status:is_first_child 3 1998.8 77990 3025.7
## + ethnic_group:parent_marital_status 11 1600.7 74391 3025.8
## + ethnic_group:wkly_study_hours 8 727.9 75264 3026.7
## + ethnic_group:parent_educ 20 2203.3 73788 3039.0
## - gender 1 12874.8 88866 3106.7
##
## Step: AIC=3015.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 112.2 77019 3014.3
## - is_first_child:transport_means 1 131.0 77038 3014.4
## - test_prep:transport_means 1 140.5 77048 3014.5
## - parent_educ:is_first_child 5 1213.8 78121 3014.7
## - test_prep:practice_sport 2 447.6 77355 3014.9
## <none> 76907 3015.4
## - test_prep:wkly_study_hours 2 530.7 77438 3015.5
## - lunch_type:wkly_study_hours 2 537.6 77445 3015.6
## - lunch_type:test_prep 1 292.2 77199 3015.7
## - parent_marital_status:transport_means 3 855.9 77763 3016.0
## - parent_educ:parent_marital_status 15 4099.1 81006 3016.1
## - lunch_type:transport_means 1 378.0 77285 3016.3
## + practice_sport:wkly_study_hours 4 915.5 75992 3016.4
## + test_prep:is_first_child 1 98.9 76808 3016.7
## + gender:is_first_child 1 98.6 76808 3016.7
## - ethnic_group:transport_means 4 1240.6 78148 3016.9
## + gender:practice_sport 2 316.3 76591 3017.0
## + gender:transport_means 1 46.6 76860 3017.1
## + gender:test_prep 1 42.4 76865 3017.1
## + is_first_child:wkly_study_hours 2 284.8 76622 3017.2
## + gender:lunch_type 1 6.1 76901 3017.4
## + gender:wkly_study_hours 2 223.6 76683 3017.7
## + transport_means:wkly_study_hours 2 181.5 76726 3018.0
## + practice_sport:transport_means 2 74.7 76832 3018.9
## + practice_sport:is_first_child 2 50.1 76857 3019.1
## + ethnic_group:test_prep 4 485.1 76422 3019.7
## + test_prep:parent_marital_status 3 175.0 76732 3020.1
## + ethnic_group:lunch_type 4 427.3 76480 3020.2
## + parent_educ:transport_means 5 659.0 76248 3020.4
## + ethnic_group:is_first_child 4 398.8 76508 3020.4
## + lunch_type:parent_marital_status 3 136.8 76770 3020.4
## + gender:parent_marital_status 3 70.3 76837 3020.9
## + parent_educ:practice_sport 10 1831.0 75076 3021.2
## + parent_educ:lunch_type 5 538.8 76368 3021.3
## - parent_marital_status:wkly_study_hours 6 2382.5 79290 3021.4
## + gender:parent_educ 5 483.0 76424 3021.7
## + gender:ethnic_group 4 222.0 76685 3021.7
## - lunch_type:practice_sport 2 1420.3 78327 3022.2
## + parent_marital_status:practice_sport 6 507.1 76400 3023.5
## + ethnic_group:practice_sport 8 971.4 75936 3023.9
## - parent_marital_status:is_first_child 3 1939.7 78847 3024.1
## + parent_educ:test_prep 5 141.9 76765 3024.3
## + parent_educ:wkly_study_hours 10 1326.1 75581 3025.2
## + ethnic_group:wkly_study_hours 8 766.2 76141 3025.5
## + ethnic_group:parent_marital_status 11 1519.3 75388 3025.7
## + ethnic_group:parent_educ 20 2096.4 74811 3039.1
## - gender 1 12541.2 89448 3102.6
##
## Step: AIC=3014.3
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 124.8 77144 3013.2
## - is_first_child:transport_means 1 128.6 77148 3013.3
## - parent_educ:is_first_child 5 1211.9 78231 3013.5
## - test_prep:practice_sport 2 461.2 77481 3013.8
## - test_prep:wkly_study_hours 2 519.7 77539 3014.3
## <none> 77019 3014.3
## - lunch_type:wkly_study_hours 2 554.4 77574 3014.5
## - lunch_type:test_prep 1 300.8 77320 3014.6
## - parent_marital_status:transport_means 3 840.4 77860 3014.7
## - lunch_type:transport_means 1 363.1 77382 3015.1
## - parent_educ:parent_marital_status 15 4150.6 81170 3015.3
## + lunch_type:is_first_child 1 112.2 76907 3015.4
## + test_prep:is_first_child 1 111.9 76907 3015.4
## + gender:is_first_child 1 87.1 76932 3015.6
## + practice_sport:wkly_study_hours 4 861.7 76158 3015.7
## + gender:practice_sport 2 343.3 76676 3015.7
## - ethnic_group:transport_means 4 1239.7 78259 3015.7
## + is_first_child:wkly_study_hours 2 316.6 76703 3015.9
## + gender:transport_means 1 38.4 76981 3016.0
## + gender:test_prep 1 38.3 76981 3016.0
## + gender:lunch_type 1 7.9 77011 3016.2
## + gender:wkly_study_hours 2 220.2 76799 3016.6
## + transport_means:wkly_study_hours 2 189.0 76830 3016.8
## + practice_sport:transport_means 2 81.6 76938 3017.7
## + practice_sport:is_first_child 2 54.8 76965 3017.9
## + ethnic_group:test_prep 4 488.8 76530 3018.5
## + ethnic_group:is_first_child 4 441.0 76578 3018.9
## + test_prep:parent_marital_status 3 175.7 76844 3018.9
## + ethnic_group:lunch_type 4 416.5 76603 3019.1
## + lunch_type:parent_marital_status 3 133.8 76886 3019.3
## + parent_educ:transport_means 5 649.1 76370 3019.3
## + gender:parent_marital_status 3 64.9 76954 3019.8
## + parent_educ:practice_sport 10 1810.2 75209 3020.3
## + parent_educ:lunch_type 5 522.4 76497 3020.3
## + gender:ethnic_group 4 235.2 76784 3020.5
## + gender:parent_educ 5 491.0 76528 3020.5
## - parent_marital_status:wkly_study_hours 6 2433.8 79453 3020.7
## - lunch_type:practice_sport 2 1430.6 78450 3021.2
## + ethnic_group:practice_sport 8 970.5 76049 3022.8
## + parent_marital_status:practice_sport 6 428.5 76591 3023.0
## + parent_educ:test_prep 5 143.4 76876 3023.2
## - parent_marital_status:is_first_child 3 2057.4 79077 3023.8
## + parent_educ:wkly_study_hours 10 1304.5 75715 3024.2
## + ethnic_group:wkly_study_hours 8 774.1 76245 3024.3
## + ethnic_group:parent_marital_status 11 1464.4 75555 3025.0
## + ethnic_group:parent_educ 20 2101.3 74918 3038.0
## - gender 1 12517.3 89537 3101.2
##
## Step: AIC=3013.25
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - is_first_child:transport_means 1 144.1 77288 3012.3
## - parent_educ:is_first_child 5 1232.2 78376 3012.6
## - test_prep:practice_sport 2 465.7 77610 3012.8
## - lunch_type:wkly_study_hours 2 493.4 77638 3013.0
## - test_prep:wkly_study_hours 2 504.4 77648 3013.1
## <none> 77144 3013.2
## - lunch_type:test_prep 1 306.8 77451 3013.6
## - parent_marital_status:transport_means 3 855.0 77999 3013.8
## - lunch_type:transport_means 1 345.9 77490 3013.9
## + test_prep:transport_means 1 124.8 77019 3014.3
## + test_prep:is_first_child 1 112.4 77032 3014.4
## + lunch_type:is_first_child 1 96.5 77048 3014.5
## + gender:is_first_child 1 90.9 77053 3014.6
## + practice_sport:wkly_study_hours 4 867.3 76277 3014.6
## + is_first_child:wkly_study_hours 2 335.0 76809 3014.7
## + gender:practice_sport 2 333.9 76810 3014.7
## - parent_educ:parent_marital_status 15 4230.9 81375 3014.8
## + gender:transport_means 1 51.1 77093 3014.9
## + gender:test_prep 1 33.7 77110 3015.0
## - ethnic_group:transport_means 4 1302.9 78447 3015.1
## + gender:lunch_type 1 11.5 77133 3015.2
## + gender:wkly_study_hours 2 229.6 76915 3015.5
## + transport_means:wkly_study_hours 2 164.7 76979 3016.0
## + practice_sport:transport_means 2 74.8 77069 3016.7
## + practice_sport:is_first_child 2 51.2 77093 3016.9
## + ethnic_group:test_prep 4 518.1 76626 3017.3
## + test_prep:parent_marital_status 3 193.8 76950 3017.8
## + ethnic_group:lunch_type 4 426.6 76718 3018.0
## + parent_educ:transport_means 5 682.3 76462 3018.0
## + ethnic_group:is_first_child 4 417.4 76727 3018.1
## + lunch_type:parent_marital_status 3 140.0 77004 3018.2
## + gender:parent_marital_status 3 62.0 77082 3018.8
## + parent_educ:lunch_type 5 527.7 76616 3019.2
## + parent_educ:practice_sport 10 1795.9 75348 3019.3
## + gender:ethnic_group 4 244.1 76900 3019.4
## + gender:parent_educ 5 499.9 76644 3019.4
## - parent_marital_status:wkly_study_hours 6 2412.6 79557 3019.4
## - lunch_type:practice_sport 2 1455.1 78599 3020.3
## + ethnic_group:practice_sport 8 984.2 76160 3021.7
## + parent_marital_status:practice_sport 6 418.9 76725 3022.0
## + parent_educ:test_prep 5 144.9 76999 3022.1
## - parent_marital_status:is_first_child 3 2069.6 79214 3022.9
## + parent_educ:wkly_study_hours 10 1307.3 75837 3023.2
## + ethnic_group:wkly_study_hours 8 770.1 76374 3023.3
## + ethnic_group:parent_marital_status 11 1459.7 75684 3024.0
## + ethnic_group:parent_educ 20 2023.1 75121 3037.6
## - gender 1 12401.3 89545 3099.2
##
## Step: AIC=3012.35
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 469.3 77757 3011.9
## - parent_educ:is_first_child 5 1272.3 78560 3012.0
## - test_prep:wkly_study_hours 2 508.1 77796 3012.2
## - lunch_type:wkly_study_hours 2 524.0 77812 3012.3
## <none> 77288 3012.3
## - lunch_type:test_prep 1 272.9 77561 3012.4
## - lunch_type:transport_means 1 336.5 77625 3012.9
## + is_first_child:transport_means 1 144.1 77144 3013.2
## + test_prep:transport_means 1 140.3 77148 3013.3
## + test_prep:is_first_child 1 122.9 77165 3013.4
## + lunch_type:is_first_child 1 93.2 77195 3013.6
## + gender:practice_sport 2 346.5 76942 3013.7
## - parent_marital_status:transport_means 3 971.0 78259 3013.7
## + gender:is_first_child 1 78.7 77209 3013.8
## + practice_sport:wkly_study_hours 4 859.2 76429 3013.8
## - parent_educ:parent_marital_status 15 4238.5 81527 3013.8
## + gender:transport_means 1 62.3 77226 3013.9
## + is_first_child:wkly_study_hours 2 301.1 76987 3014.1
## + gender:test_prep 1 30.1 77258 3014.1
## + gender:lunch_type 1 8.4 77280 3014.3
## - ethnic_group:transport_means 4 1313.4 78602 3014.3
## + gender:wkly_study_hours 2 218.6 77070 3014.7
## + transport_means:wkly_study_hours 2 163.3 77125 3015.1
## + practice_sport:transport_means 2 89.4 77199 3015.7
## + practice_sport:is_first_child 2 64.9 77223 3015.9
## + ethnic_group:test_prep 4 542.2 76746 3016.2
## + test_prep:parent_marital_status 3 183.1 77105 3016.9
## + ethnic_group:lunch_type 4 413.2 76875 3017.2
## + lunch_type:parent_marital_status 3 139.1 77149 3017.3
## + parent_educ:transport_means 5 635.8 76652 3017.5
## + gender:parent_marital_status 3 80.3 77208 3017.7
## + ethnic_group:is_first_child 4 330.6 76958 3017.8
## + parent_educ:lunch_type 5 529.8 76758 3018.3
## + gender:ethnic_group 4 247.6 77041 3018.5
## + gender:parent_educ 5 496.8 76791 3018.6
## - parent_marital_status:wkly_study_hours 6 2429.0 79717 3018.6
## + parent_educ:practice_sport 10 1711.9 75576 3019.1
## - lunch_type:practice_sport 2 1445.6 78734 3019.3
## + ethnic_group:practice_sport 8 1012.9 76275 3020.6
## + parent_educ:test_prep 5 179.0 77109 3021.0
## + parent_marital_status:practice_sport 6 437.9 76850 3021.0
## - parent_marital_status:is_first_child 3 2038.1 79326 3021.7
## + parent_educ:wkly_study_hours 10 1301.9 75986 3022.3
## + ethnic_group:wkly_study_hours 8 781.1 76507 3022.4
## + ethnic_group:parent_marital_status 11 1531.4 75757 3022.6
## + ethnic_group:parent_educ 20 1990.8 75297 3037.0
## - gender 1 12297.8 89586 3097.5
##
## Step: AIC=3011.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 503.4 78261 3011.7
## <none> 77757 3011.9
## - lunch_type:test_prep 1 290.1 78048 3012.1
## - lunch_type:transport_means 1 318.4 78076 3012.3
## + test_prep:practice_sport 2 469.3 77288 3012.3
## - lunch_type:wkly_study_hours 2 588.6 78346 3012.4
## - parent_educ:parent_marital_status 15 4157.8 81915 3012.7
## + is_first_child:transport_means 1 147.6 77610 3012.8
## + test_prep:transport_means 1 145.3 77612 3012.8
## + test_prep:is_first_child 1 122.2 77635 3013.0
## + gender:practice_sport 2 383.7 77374 3013.0
## - parent_educ:is_first_child 5 1477.9 79235 3013.0
## - parent_marital_status:transport_means 3 950.8 78708 3013.1
## + lunch_type:is_first_child 1 106.0 77652 3013.1
## + practice_sport:wkly_study_hours 4 891.5 76866 3013.1
## - ethnic_group:transport_means 4 1242.4 79000 3013.3
## + gender:is_first_child 1 59.5 77698 3013.5
## + gender:transport_means 1 54.2 77703 3013.5
## + gender:test_prep 1 25.3 77732 3013.7
## + gender:lunch_type 1 15.2 77742 3013.8
## + is_first_child:wkly_study_hours 2 265.7 77492 3013.9
## + transport_means:wkly_study_hours 2 199.8 77558 3014.4
## + gender:wkly_study_hours 2 198.7 77559 3014.4
## + practice_sport:is_first_child 2 85.8 77672 3015.3
## + practice_sport:transport_means 2 82.6 77675 3015.3
## + test_prep:parent_marital_status 3 234.8 77523 3016.1
## + ethnic_group:lunch_type 4 460.3 77297 3016.4
## + ethnic_group:test_prep 4 451.0 77306 3016.5
## + lunch_type:parent_marital_status 3 142.6 77615 3016.8
## + parent_educ:transport_means 5 666.7 77091 3016.8
## + gender:parent_marital_status 3 101.5 77656 3017.2
## + ethnic_group:is_first_child 4 337.2 77420 3017.4
## - parent_marital_status:wkly_study_hours 6 2359.6 80117 3017.6
## + parent_educ:lunch_type 5 553.5 77204 3017.7
## + gender:parent_educ 5 531.7 77226 3017.9
## + gender:ethnic_group 4 217.0 77540 3018.3
## + parent_educ:practice_sport 10 1673.0 76084 3019.1
## - lunch_type:practice_sport 2 1545.1 79303 3019.5
## - parent_marital_status:is_first_child 3 1928.4 79686 3020.4
## + ethnic_group:practice_sport 8 981.3 76776 3020.4
## + parent_marital_status:practice_sport 6 444.5 77313 3020.5
## + parent_educ:test_prep 5 146.8 77611 3020.8
## + parent_educ:wkly_study_hours 10 1371.1 76386 3021.4
## + ethnic_group:wkly_study_hours 8 769.9 76988 3022.1
## + ethnic_group:parent_marital_status 11 1497.6 76260 3022.4
## + ethnic_group:parent_educ 20 2102.3 75655 3035.8
## - gender 1 12364.6 90122 3097.0
##
## Step: AIC=3011.73
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 221.7 78483 3011.4
## <none> 78261 3011.7
## + test_prep:wkly_study_hours 2 503.4 77757 3011.9
## - parent_educ:parent_marital_status 15 4125.9 82387 3012.0
## - lunch_type:test_prep 1 312.1 78573 3012.1
## + test_prep:practice_sport 2 464.6 77796 3012.2
## - ethnic_group:transport_means 4 1170.1 79431 3012.5
## + practice_sport:wkly_study_hours 4 942.3 77319 3012.6
## + is_first_child:transport_means 1 151.9 78109 3012.6
## - lunch_type:wkly_study_hours 2 649.4 78910 3012.6
## + test_prep:transport_means 1 129.4 78132 3012.8
## + test_prep:is_first_child 1 116.8 78144 3012.8
## - parent_marital_status:transport_means 3 952.4 79213 3012.9
## - parent_educ:is_first_child 5 1493.3 79754 3012.9
## + gender:practice_sport 2 370.4 77890 3012.9
## + lunch_type:is_first_child 1 98.9 78162 3013.0
## + gender:transport_means 1 60.3 78201 3013.3
## + gender:is_first_child 1 51.3 78210 3013.3
## + gender:lunch_type 1 22.1 78239 3013.6
## + gender:test_prep 1 14.9 78246 3013.6
## + is_first_child:wkly_study_hours 2 273.1 77988 3013.7
## + gender:wkly_study_hours 2 195.1 78066 3014.3
## + transport_means:wkly_study_hours 2 185.5 78075 3014.3
## + practice_sport:transport_means 2 85.5 78175 3015.1
## + practice_sport:is_first_child 2 56.2 78205 3015.3
## + ethnic_group:test_prep 4 507.3 77754 3015.9
## + test_prep:parent_marital_status 3 218.3 78043 3016.1
## + ethnic_group:lunch_type 4 477.5 77783 3016.1
## + parent_educ:transport_means 5 668.9 77592 3016.7
## + lunch_type:parent_marital_status 3 124.1 78137 3016.8
## + gender:parent_marital_status 3 110.8 78150 3016.9
## - parent_marital_status:wkly_study_hours 6 2347.2 80608 3017.2
## + gender:parent_educ 5 531.0 77730 3017.7
## + parent_educ:lunch_type 5 527.0 77734 3017.8
## + gender:ethnic_group 4 259.9 78001 3017.8
## + ethnic_group:is_first_child 4 236.4 78024 3017.9
## - lunch_type:practice_sport 2 1430.9 79692 3018.4
## + parent_marital_status:practice_sport 6 469.5 77791 3020.2
## + parent_educ:practice_sport 10 1509.6 76751 3020.2
## + parent_educ:test_prep 5 187.2 78074 3020.3
## + parent_educ:wkly_study_hours 10 1467.4 76794 3020.6
## - parent_marital_status:is_first_child 3 2024.8 80286 3020.8
## + ethnic_group:practice_sport 8 898.6 77362 3020.9
## + ethnic_group:parent_marital_status 11 1610.1 76651 3021.5
## + ethnic_group:wkly_study_hours 8 778.1 77483 3021.8
## + ethnic_group:parent_educ 20 2152.2 76109 3035.3
## - gender 1 12415.3 90676 3096.6
##
## Step: AIC=3011.4
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 262.1 78745 3011.4
## <none> 78483 3011.4
## - parent_educ:parent_marital_status 15 4130.4 82613 3011.7
## + lunch_type:transport_means 1 221.7 78261 3011.7
## + test_prep:practice_sport 2 449.9 78033 3012.0
## - ethnic_group:transport_means 4 1161.5 79644 3012.1
## - lunch_type:wkly_study_hours 2 628.3 79111 3012.1
## - parent_educ:is_first_child 5 1457.2 79940 3012.2
## + test_prep:is_first_child 1 146.9 78336 3012.3
## + is_first_child:transport_means 1 144.0 78339 3012.3
## + test_prep:wkly_study_hours 2 406.7 78076 3012.3
## + gender:practice_sport 2 390.3 78092 3012.5
## + test_prep:transport_means 1 116.1 78367 3012.5
## - parent_marital_status:transport_means 3 954.6 79437 3012.5
## + practice_sport:wkly_study_hours 4 897.3 77585 3012.6
## + lunch_type:is_first_child 1 89.8 78393 3012.7
## + gender:transport_means 1 71.0 78412 3012.9
## + gender:is_first_child 1 67.6 78415 3012.9
## + gender:lunch_type 1 31.1 78451 3013.2
## + gender:test_prep 1 21.5 78461 3013.2
## + is_first_child:wkly_study_hours 2 272.3 78210 3013.3
## + gender:wkly_study_hours 2 197.2 78285 3013.9
## + transport_means:wkly_study_hours 2 171.9 78311 3014.1
## + practice_sport:transport_means 2 92.0 78391 3014.7
## + practice_sport:is_first_child 2 53.0 78430 3015.0
## + ethnic_group:lunch_type 4 533.7 77949 3015.4
## + ethnic_group:test_prep 4 514.6 77968 3015.5
## + test_prep:parent_marital_status 3 224.0 78259 3015.7
## + gender:parent_marital_status 3 140.6 78342 3016.3
## + parent_educ:transport_means 5 664.5 77818 3016.4
## + lunch_type:parent_marital_status 3 128.4 78354 3016.4
## + gender:parent_educ 5 587.5 77895 3017.0
## - parent_marital_status:wkly_study_hours 6 2395.3 80878 3017.1
## + parent_educ:lunch_type 5 559.6 77923 3017.2
## + gender:ethnic_group 4 256.9 78226 3017.5
## + ethnic_group:is_first_child 4 221.7 78261 3017.7
## - lunch_type:practice_sport 2 1393.9 79876 3017.8
## + parent_marital_status:practice_sport 6 467.3 78015 3019.9
## + parent_educ:test_prep 5 194.3 78288 3019.9
## + parent_educ:practice_sport 10 1487.5 76995 3020.1
## + parent_educ:wkly_study_hours 10 1441.2 77041 3020.5
## - parent_marital_status:is_first_child 3 2065.7 80548 3020.7
## + ethnic_group:parent_marital_status 11 1648.0 76835 3020.9
## + ethnic_group:practice_sport 8 846.7 77636 3021.0
## + ethnic_group:wkly_study_hours 8 744.7 77738 3021.8
## + ethnic_group:parent_educ 20 2158.3 76324 3034.9
## - gender 1 12321.2 90804 3095.4
##
## Step: AIC=3011.37
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 15 4063.4 82808 3011.1
## <none> 78745 3011.4
## + lunch_type:test_prep 1 262.1 78483 3011.4
## - lunch_type:wkly_study_hours 2 575.8 79321 3011.7
## + test_prep:practice_sport 2 468.3 78276 3011.8
## - parent_educ:is_first_child 5 1428.4 80173 3012.0
## - ethnic_group:transport_means 4 1168.4 79913 3012.1
## + lunch_type:transport_means 1 171.7 78573 3012.1
## + test_prep:wkly_study_hours 2 435.1 78310 3012.1
## + practice_sport:wkly_study_hours 4 949.3 77795 3012.2
## - parent_marital_status:transport_means 3 939.6 79684 3012.4
## + test_prep:is_first_child 1 129.3 78615 3012.4
## + test_prep:transport_means 1 121.3 78623 3012.5
## + gender:practice_sport 2 386.6 78358 3012.5
## + is_first_child:transport_means 1 112.6 78632 3012.5
## + lunch_type:is_first_child 1 100.4 78644 3012.6
## + gender:is_first_child 1 76.3 78668 3012.8
## + gender:transport_means 1 74.0 78671 3012.8
## + gender:lunch_type 1 46.0 78699 3013.0
## + is_first_child:wkly_study_hours 2 312.2 78432 3013.0
## + gender:test_prep 1 29.1 78716 3013.2
## + gender:wkly_study_hours 2 197.1 78548 3013.9
## + transport_means:wkly_study_hours 2 173.8 78571 3014.1
## + practice_sport:transport_means 2 114.1 78631 3014.5
## + practice_sport:is_first_child 2 62.2 78683 3014.9
## + ethnic_group:lunch_type 4 561.7 78183 3015.1
## + ethnic_group:test_prep 4 525.1 78220 3015.4
## + test_prep:parent_marital_status 3 228.3 78516 3015.7
## + parent_educ:transport_means 5 680.5 78064 3016.2
## + gender:parent_marital_status 3 140.2 78604 3016.3
## + lunch_type:parent_marital_status 3 119.1 78626 3016.5
## + gender:parent_educ 5 618.2 78126 3016.7
## + parent_educ:lunch_type 5 559.3 78185 3017.2
## - parent_marital_status:wkly_study_hours 6 2417.6 81162 3017.2
## + gender:ethnic_group 4 269.6 78475 3017.3
## + ethnic_group:is_first_child 4 245.7 78499 3017.5
## - lunch_type:practice_sport 2 1369.3 80114 3017.5
## + parent_educ:practice_sport 10 1524.1 77221 3019.8
## + parent_educ:wkly_study_hours 10 1522.8 77222 3019.8
## + parent_marital_status:practice_sport 6 467.4 78277 3019.9
## + parent_educ:test_prep 5 186.3 78558 3020.0
## + ethnic_group:practice_sport 8 913.7 77831 3020.5
## - parent_marital_status:is_first_child 3 2115.1 80860 3021.0
## + ethnic_group:wkly_study_hours 8 829.7 77915 3021.1
## + ethnic_group:parent_marital_status 11 1564.4 77180 3021.5
## + ethnic_group:parent_educ 20 2215.7 76529 3034.5
## - test_prep 1 9863.4 88608 3079.0
## - gender 1 12254.8 91000 3094.7
##
## Step: AIC=3011.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:is_first_child + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 657.5 83466 3009.7
## - parent_educ:is_first_child 5 1407.4 84216 3011.0
## <none> 82808 3011.1
## + parent_educ:parent_marital_status 15 4063.4 78745 3011.4
## + test_prep:transport_means 1 195.2 82613 3011.7
## + lunch_type:test_prep 1 195.1 82613 3011.7
## + gender:practice_sport 2 473.7 82334 3011.7
## + lunch_type:transport_means 1 185.2 82623 3011.7
## - ethnic_group:transport_means 4 1252.3 84060 3011.9
## + lunch_type:is_first_child 1 148.1 82660 3012.0
## + is_first_child:transport_means 1 126.7 82681 3012.2
## + test_prep:is_first_child 1 126.1 82682 3012.2
## + test_prep:wkly_study_hours 2 396.1 82412 3012.2
## - lunch_type:wkly_study_hours 2 731.3 83539 3012.2
## + test_prep:practice_sport 2 380.1 82428 3012.3
## + gender:is_first_child 1 70.3 82738 3012.6
## + is_first_child:wkly_study_hours 2 345.7 82462 3012.6
## + practice_sport:wkly_study_hours 4 881.8 81926 3012.7
## + gender:transport_means 1 38.6 82770 3012.8
## + gender:lunch_type 1 36.2 82772 3012.8
## + gender:test_prep 1 12.1 82796 3013.0
## + gender:wkly_study_hours 2 277.5 82531 3013.1
## + transport_means:wkly_study_hours 2 155.0 82653 3013.9
## + practice_sport:transport_means 2 76.8 82731 3014.5
## + gender:parent_educ 5 878.7 81929 3014.8
## + practice_sport:is_first_child 2 21.4 82787 3014.9
## - parent_marital_status:wkly_study_hours 6 2271.7 85080 3015.0
## - lunch_type:practice_sport 2 1129.5 83938 3015.1
## + lunch_type:parent_marital_status 3 198.0 82610 3015.6
## + ethnic_group:test_prep 4 455.0 82353 3015.8
## + parent_educ:wkly_study_hours 10 2108.4 80700 3015.8
## - parent_marital_status:is_first_child 3 1546.8 84355 3016.0
## + test_prep:parent_marital_status 3 138.0 82670 3016.1
## + gender:parent_marital_status 3 117.4 82691 3016.2
## + parent_educ:transport_means 5 654.1 82154 3016.4
## + gender:ethnic_group 4 364.0 82444 3016.4
## + ethnic_group:lunch_type 4 347.8 82460 3016.6
## + ethnic_group:is_first_child 4 240.9 82567 3017.3
## + parent_educ:lunch_type 5 513.6 82295 3017.4
## + parent_marital_status:practice_sport 6 744.7 82063 3017.7
## + parent_educ:practice_sport 10 1768.3 81040 3018.3
## + parent_educ:test_prep 5 292.1 82516 3019.0
## + ethnic_group:practice_sport 8 1100.3 81708 3019.2
## + ethnic_group:parent_marital_status 11 1823.4 80985 3019.9
## + ethnic_group:wkly_study_hours 8 839.1 81969 3021.1
## + ethnic_group:parent_educ 20 2212.2 80596 3035.1
## - test_prep 1 9566.9 92375 3073.6
## - gender 1 12656.8 95465 3093.0
##
## Step: AIC=3009.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:is_first_child + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:is_first_child 5 1301.6 84767 3008.8
## <none> 83466 3009.7
## - ethnic_group:transport_means 4 1174.0 84640 3010.0
## + test_prep:transport_means 1 229.8 83236 3010.1
## + is_first_child:transport_means 1 215.1 83251 3010.2
## + lunch_type:test_prep 1 186.9 83279 3010.4
## + lunch_type:transport_means 1 186.6 83279 3010.4
## - lunch_type:wkly_study_hours 2 708.4 84174 3010.7
## + lunch_type:is_first_child 1 131.4 83334 3010.8
## + test_prep:is_first_child 1 127.4 83338 3010.8
## + gender:practice_sport 2 407.4 83058 3010.8
## + gender:is_first_child 1 96.5 83369 3011.0
## + parent_marital_status:transport_means 3 657.5 82808 3011.1
## + test_prep:wkly_study_hours 2 375.5 83090 3011.1
## + test_prep:practice_sport 2 375.2 83090 3011.1
## + gender:transport_means 1 31.2 83435 3011.5
## + gender:lunch_type 1 24.1 83442 3011.6
## + gender:test_prep 1 17.3 83448 3011.6
## + practice_sport:wkly_study_hours 4 858.9 82607 3011.6
## + gender:wkly_study_hours 2 280.1 83186 3011.7
## + is_first_child:wkly_study_hours 2 278.3 83187 3011.8
## + parent_educ:parent_marital_status 15 3781.3 79684 3012.4
## - parent_marital_status:wkly_study_hours 6 2151.2 85617 3012.7
## + transport_means:wkly_study_hours 2 134.1 83332 3012.8
## + gender:parent_educ 5 969.9 82496 3012.8
## + practice_sport:transport_means 2 108.4 83357 3012.9
## + practice_sport:is_first_child 2 9.9 83456 3013.7
## + test_prep:parent_marital_status 3 220.3 83245 3014.2
## + parent_educ:wkly_study_hours 10 2160.5 81305 3014.2
## + lunch_type:parent_marital_status 3 191.9 83274 3014.4
## - lunch_type:practice_sport 2 1249.9 84716 3014.5
## + gender:parent_marital_status 3 129.0 83337 3014.8
## + gender:ethnic_group 4 409.1 83057 3014.8
## + ethnic_group:test_prep 4 400.2 83065 3014.9
## - parent_marital_status:is_first_child 3 1618.7 85084 3015.1
## + parent_educ:transport_means 5 613.7 82852 3015.4
## + ethnic_group:lunch_type 4 331.8 83134 3015.4
## + parent_educ:lunch_type 5 499.0 82967 3016.2
## + parent_educ:practice_sport 10 1891.8 81574 3016.2
## + ethnic_group:is_first_child 4 190.0 83276 3016.4
## + parent_marital_status:practice_sport 6 751.8 82714 3016.4
## + ethnic_group:practice_sport 8 1191.8 82274 3017.2
## + parent_educ:test_prep 5 302.8 83163 3017.6
## + ethnic_group:parent_marital_status 11 1930.5 81535 3017.9
## + ethnic_group:wkly_study_hours 8 816.2 82649 3019.9
## + ethnic_group:parent_educ 20 2008.0 81458 3035.3
## - test_prep 1 9947.6 93413 3074.2
## - gender 1 12642.9 96109 3090.9
##
## Step: AIC=3008.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 84767 3008.8
## + test_prep:transport_means 1 263.6 84504 3009.0
## + test_prep:practice_sport 2 543.3 84224 3009.1
## + is_first_child:transport_means 1 254.5 84513 3009.1
## - ethnic_group:transport_means 4 1232.7 86000 3009.4
## - lunch_type:wkly_study_hours 2 680.0 85447 3009.6
## + lunch_type:test_prep 1 164.4 84603 3009.7
## + parent_educ:is_first_child 5 1301.6 83466 3009.7
## + lunch_type:transport_means 1 139.2 84628 3009.9
## + lunch_type:is_first_child 1 125.4 84642 3010.0
## + gender:practice_sport 2 401.7 84366 3010.1
## + gender:is_first_child 1 108.5 84659 3010.1
## + test_prep:wkly_study_hours 2 383.2 84384 3010.2
## + test_prep:is_first_child 1 63.8 84704 3010.4
## + gender:lunch_type 1 22.9 84744 3010.7
## + gender:transport_means 1 19.0 84748 3010.7
## + gender:test_prep 1 5.3 84762 3010.8
## + parent_marital_status:transport_means 3 551.7 84216 3011.0
## - parent_marital_status:wkly_study_hours 6 2060.3 86828 3011.0
## + gender:wkly_study_hours 2 232.3 84535 3011.2
## + is_first_child:wkly_study_hours 2 193.2 84574 3011.5
## + parent_educ:parent_marital_status 15 3818.8 80949 3011.7
## + transport_means:wkly_study_hours 2 107.3 84660 3012.1
## + practice_sport:transport_means 2 103.2 84664 3012.1
## + practice_sport:wkly_study_hours 4 671.8 84096 3012.2
## - parent_marital_status:is_first_child 3 1395.1 86162 3012.5
## + gender:parent_educ 5 882.7 83885 3012.7
## + practice_sport:is_first_child 2 3.9 84763 3012.8
## + test_prep:parent_marital_status 3 189.7 84578 3013.5
## - lunch_type:practice_sport 2 1258.7 86026 3013.6
## + ethnic_group:test_prep 4 470.3 84297 3013.6
## + lunch_type:parent_marital_status 3 184.0 84583 3013.6
## + gender:ethnic_group 4 464.8 84303 3013.6
## + parent_educ:practice_sport 10 2151.4 82616 3013.7
## + ethnic_group:lunch_type 4 388.3 84379 3014.1
## + gender:parent_marital_status 3 70.7 84697 3014.4
## + parent_educ:wkly_study_hours 10 2035.7 82732 3014.5
## + parent_educ:transport_means 5 615.3 84152 3014.6
## + parent_marital_status:practice_sport 6 773.3 83994 3015.4
## + parent_educ:lunch_type 5 477.7 84290 3015.5
## + ethnic_group:is_first_child 4 188.4 84579 3015.5
## + parent_educ:test_prep 5 338.3 84429 3016.5
## + ethnic_group:practice_sport 8 1107.8 83660 3017.1
## + ethnic_group:parent_marital_status 11 1856.5 82911 3017.8
## + ethnic_group:wkly_study_hours 8 765.8 84002 3019.5
## + ethnic_group:parent_educ 20 2002.1 82765 3034.8
## - parent_educ 5 9294.5 94062 3060.2
## - test_prep 1 9780.6 94548 3071.3
## - gender 1 12516.7 97284 3088.1summary(stepwise_model_write)##
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours,
## data = df_4_mdl_write)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.763 -7.903 0.888 8.581 28.915
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 67.70191 5.43878
## gendermale -9.60342 1.06468
## ethnic_groupgroup B 2.66505 3.60266
## ethnic_groupgroup C 4.66371 3.29737
## ethnic_groupgroup D 6.89890 3.37504
## ethnic_groupgroup E 12.97757 3.72825
## parent_educbachelor's degree 3.78448 1.87145
## parent_educhigh school -6.78406 1.62165
## parent_educmaster's degree 5.13686 2.33681
## parent_educsome college -1.61594 1.62678
## parent_educsome high school -6.56468 1.63632
## lunch_typestandard 1.01145 3.66619
## test_prepnone -8.81344 1.10535
## parent_marital_statusmarried 7.41012 3.91977
## parent_marital_statussingle -3.99879 4.28335
## parent_marital_statuswidowed 12.38775 10.44238
## practice_sportregularly -3.44862 3.11402
## practice_sportsometimes -5.25858 3.01623
## is_first_childyes 6.17523 3.24819
## transport_meansschool_bus 5.99682 3.71242
## wkly_study_hours> 10 -13.41677 4.87463
## wkly_study_hours10-May -1.32300 3.52689
## ethnic_groupgroup B:transport_meansschool_bus -6.38307 4.47966
## ethnic_groupgroup C:transport_meansschool_bus -7.47646 4.19267
## ethnic_groupgroup D:transport_meansschool_bus -2.44868 4.26882
## ethnic_groupgroup E:transport_meansschool_bus -10.30293 4.71351
## lunch_typestandard:practice_sportregularly 6.16137 3.77036
## lunch_typestandard:practice_sportsometimes 10.02195 3.67485
## lunch_typestandard:wkly_study_hours> 10 5.91877 3.33331
## lunch_typestandard:wkly_study_hours10-May -0.07475 2.59512
## parent_marital_statusmarried:is_first_childyes -7.62546 3.55928
## parent_marital_statussingle:is_first_childyes -0.73567 3.95710
## parent_marital_statuswidowed:is_first_childyes -5.74724 8.37846
## parent_marital_statusmarried:wkly_study_hours> 10 10.26572 4.74053
## parent_marital_statussingle:wkly_study_hours> 10 18.67985 5.30411
## parent_marital_statuswidowed:wkly_study_hours> 10 5.92668 13.84492
## parent_marital_statusmarried:wkly_study_hours10-May 3.32999 3.53309
## parent_marital_statussingle:wkly_study_hours10-May 8.29920 3.98905
## parent_marital_statuswidowed:wkly_study_hours10-May -0.28438 10.39843
## t value Pr(>|t|)
## (Intercept) 12.448 < 2e-16 ***
## gendermale -9.020 < 2e-16 ***
## ethnic_groupgroup B 0.740 0.459770
## ethnic_groupgroup C 1.414 0.157818
## ethnic_groupgroup D 2.044 0.041419 *
## ethnic_groupgroup E 3.481 0.000539 ***
## parent_educbachelor's degree 2.022 0.043636 *
## parent_educhigh school -4.183 3.34e-05 ***
## parent_educmaster's degree 2.198 0.028347 *
## parent_educsome college -0.993 0.320980
## parent_educsome high school -4.012 6.86e-05 ***
## lunch_typestandard 0.276 0.782738
## test_prepnone -7.973 8.95e-15 ***
## parent_marital_statusmarried 1.890 0.059222 .
## parent_marital_statussingle -0.934 0.350937
## parent_marital_statuswidowed 1.186 0.236016
## practice_sportregularly -1.107 0.268583
## practice_sportsometimes -1.743 0.081816 .
## is_first_childyes 1.901 0.057806 .
## transport_meansschool_bus 1.615 0.106809
## wkly_study_hours> 10 -2.752 0.006112 **
## wkly_study_hours10-May -0.375 0.707718
## ethnic_groupgroup B:transport_meansschool_bus -1.425 0.154752
## ethnic_groupgroup C:transport_meansschool_bus -1.783 0.075100 .
## ethnic_groupgroup D:transport_meansschool_bus -0.574 0.566459
## ethnic_groupgroup E:transport_meansschool_bus -2.186 0.029248 *
## lunch_typestandard:practice_sportregularly 1.634 0.102796
## lunch_typestandard:practice_sportsometimes 2.727 0.006592 **
## lunch_typestandard:wkly_study_hours> 10 1.776 0.076344 .
## lunch_typestandard:wkly_study_hours10-May -0.029 0.977030
## parent_marital_statusmarried:is_first_childyes -2.142 0.032597 *
## parent_marital_statussingle:is_first_childyes -0.186 0.852583
## parent_marital_statuswidowed:is_first_childyes -0.686 0.493030
## parent_marital_statusmarried:wkly_study_hours> 10 2.166 0.030776 *
## parent_marital_statussingle:wkly_study_hours> 10 3.522 0.000464 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 0.428 0.668763
## parent_marital_statusmarried:wkly_study_hours10-May 0.943 0.346342
## parent_marital_statussingle:wkly_study_hours10-May 2.080 0.037941 *
## parent_marital_statuswidowed:wkly_study_hours10-May -0.027 0.978192
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.4 on 551 degrees of freedom
## Multiple R-squared: 0.4032, Adjusted R-squared: 0.362
## F-statistic: 9.796 on 38 and 551 DF, p-value: < 2.2e-16MAth Score
df_4_mdl_math=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score)
full_fit_math=lm(math_score ~ .^2,data=df_4_mdl_math)summary(full_fit_math)##
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.489 -7.390 0.168 7.221 24.154
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 68.0411 17.6110
## gendermale 4.9827 8.9723
## ethnic_groupgroup B -20.0944 15.1422
## ethnic_groupgroup C -26.3767 14.2851
## ethnic_groupgroup D -16.7609 15.5502
## ethnic_groupgroup E -2.1592 14.5735
## parent_educbachelor's degree 33.6079 15.9209
## parent_educhigh school 12.3061 13.1796
## parent_educmaster's degree -25.1426 21.7572
## parent_educsome college -3.3640 12.9319
## parent_educsome high school 1.5736 12.5441
## lunch_typestandard 2.2940 8.9077
## test_prepnone -16.5825 9.2941
## parent_marital_statusmarried 11.4586 11.8338
## parent_marital_statussingle 7.8399 14.2425
## parent_marital_statuswidowed 56.5536 42.0759
## practice_sportregularly -29.8202 14.1677
## practice_sportsometimes -20.2458 14.0961
## is_first_childyes 13.1687 10.2054
## transport_meansschool_bus -3.8403 9.0340
## wkly_study_hours> 10 -10.7976 13.9166
## wkly_study_hours10-May 4.6821 11.1838
## gendermale:ethnic_groupgroup B 5.2886 5.6833
## gendermale:ethnic_groupgroup C 10.1735 5.4655
## gendermale:ethnic_groupgroup D 4.3097 5.4293
## gendermale:ethnic_groupgroup E 6.3964 6.0199
## gendermale:parent_educbachelor's degree -4.5741 4.7806
## gendermale:parent_educhigh school 1.1545 3.8987
## gendermale:parent_educmaster's degree 11.0840 6.6935
## gendermale:parent_educsome college -4.4251 4.0942
## gendermale:parent_educsome high school 1.5882 4.0216
## gendermale:lunch_typestandard -2.4581 2.7927
## gendermale:test_prepnone 0.3238 2.7833
## gendermale:parent_marital_statusmarried -2.2028 3.9676
## gendermale:parent_marital_statussingle -1.7229 4.4981
## gendermale:parent_marital_statuswidowed -1.1049 19.4773
## gendermale:practice_sportregularly -3.5415 4.7295
## gendermale:practice_sportsometimes -3.5726 4.7543
## gendermale:is_first_childyes 2.6976 2.9215
## gendermale:transport_meansschool_bus -0.3742 2.7006
## gendermale:wkly_study_hours> 10 -3.4820 4.2367
## gendermale:wkly_study_hours10-May -1.9685 3.2131
## ethnic_groupgroup B:parent_educbachelor's degree -4.2231 13.2581
## ethnic_groupgroup C:parent_educbachelor's degree -3.7714 13.2368
## ethnic_groupgroup D:parent_educbachelor's degree -1.2605 13.1369
## ethnic_groupgroup E:parent_educbachelor's degree -9.8679 14.9506
## ethnic_groupgroup B:parent_educhigh school -12.1115 8.3005
## ethnic_groupgroup C:parent_educhigh school -7.8179 7.9780
## ethnic_groupgroup D:parent_educhigh school -4.1223 8.1111
## ethnic_groupgroup E:parent_educhigh school -7.1674 9.0331
## ethnic_groupgroup B:parent_educmaster's degree 6.1658 15.9289
## ethnic_groupgroup C:parent_educmaster's degree -5.7091 14.7953
## ethnic_groupgroup D:parent_educmaster's degree 2.3388 15.0307
## ethnic_groupgroup E:parent_educmaster's degree -0.8632 15.8151
## ethnic_groupgroup B:parent_educsome college 2.3899 9.1796
## ethnic_groupgroup C:parent_educsome college 3.2541 8.6646
## ethnic_groupgroup D:parent_educsome college 12.0158 9.0246
## ethnic_groupgroup E:parent_educsome college 1.8215 9.1236
## ethnic_groupgroup B:parent_educsome high school -15.0749 8.7983
## ethnic_groupgroup C:parent_educsome high school -4.9385 8.2551
## ethnic_groupgroup D:parent_educsome high school -1.1085 8.3094
## ethnic_groupgroup E:parent_educsome high school 2.2394 8.9218
## ethnic_groupgroup B:lunch_typestandard 3.7732 5.9098
## ethnic_groupgroup C:lunch_typestandard 7.9926 5.7317
## ethnic_groupgroup D:lunch_typestandard 4.4950 5.6419
## ethnic_groupgroup E:lunch_typestandard 0.8425 6.5383
## ethnic_groupgroup B:test_prepnone 2.4360 6.0294
## ethnic_groupgroup C:test_prepnone 7.7889 5.6560
## ethnic_groupgroup D:test_prepnone 7.7952 5.6674
## ethnic_groupgroup E:test_prepnone 11.4896 6.1691
## ethnic_groupgroup B:parent_marital_statusmarried 4.5004 8.1401
## ethnic_groupgroup C:parent_marital_statusmarried 2.5638 7.4956
## ethnic_groupgroup D:parent_marital_statusmarried -8.5771 7.3930
## ethnic_groupgroup E:parent_marital_statusmarried -2.5010 8.1793
## ethnic_groupgroup B:parent_marital_statussingle 11.3279 9.6376
## ethnic_groupgroup C:parent_marital_statussingle 3.2686 9.1120
## ethnic_groupgroup D:parent_marital_statussingle -2.3267 8.8048
## ethnic_groupgroup E:parent_marital_statussingle 6.0944 10.1485
## ethnic_groupgroup B:parent_marital_statuswidowed 112.2530 107.8327
## ethnic_groupgroup C:parent_marital_statuswidowed 143.7513 87.6384
## ethnic_groupgroup D:parent_marital_statuswidowed 31.6392 88.3465
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 18.1643 10.7978
## ethnic_groupgroup C:practice_sportregularly 15.6305 10.7005
## ethnic_groupgroup D:practice_sportregularly 15.7111 11.9445
## ethnic_groupgroup E:practice_sportregularly 16.2136 10.9347
## ethnic_groupgroup B:practice_sportsometimes 12.2733 11.5184
## ethnic_groupgroup C:practice_sportsometimes 18.8952 11.2034
## ethnic_groupgroup D:practice_sportsometimes 12.8401 12.3508
## ethnic_groupgroup E:practice_sportsometimes 11.3892 11.2604
## ethnic_groupgroup B:is_first_childyes 10.2091 5.9835
## ethnic_groupgroup C:is_first_childyes -0.1812 5.6444
## ethnic_groupgroup D:is_first_childyes 1.1359 5.7099
## ethnic_groupgroup E:is_first_childyes 3.4944 6.4312
## ethnic_groupgroup B:transport_meansschool_bus -4.0964 5.9868
## ethnic_groupgroup C:transport_meansschool_bus -10.1575 5.5281
## ethnic_groupgroup D:transport_meansschool_bus -2.9759 5.5226
## ethnic_groupgroup E:transport_meansschool_bus -11.7574 6.5192
## ethnic_groupgroup B:wkly_study_hours> 10 -10.0294 10.1919
## ethnic_groupgroup C:wkly_study_hours> 10 1.4113 10.0649
## ethnic_groupgroup D:wkly_study_hours> 10 4.1762 10.0509
## ethnic_groupgroup E:wkly_study_hours> 10 -3.4964 10.9491
## ethnic_groupgroup B:wkly_study_hours10-May -5.9718 8.5598
## ethnic_groupgroup C:wkly_study_hours10-May 2.3955 8.3758
## ethnic_groupgroup D:wkly_study_hours10-May 2.5625 8.5173
## ethnic_groupgroup E:wkly_study_hours10-May -2.6577 9.1705
## parent_educbachelor's degree:lunch_typestandard 2.1141 5.1441
## parent_educhigh school:lunch_typestandard 0.3684 4.1512
## parent_educmaster's degree:lunch_typestandard 9.9274 7.6084
## parent_educsome college:lunch_typestandard 3.3042 4.1848
## parent_educsome high school:lunch_typestandard 5.5345 4.3349
## parent_educbachelor's degree:test_prepnone -3.9833 4.7464
## parent_educhigh school:test_prepnone -1.1824 4.5458
## parent_educmaster's degree:test_prepnone -1.8200 8.0921
## parent_educsome college:test_prepnone -2.3529 4.2606
## parent_educsome high school:test_prepnone 3.0111 4.1206
## parent_educbachelor's degree:parent_marital_statusmarried -17.7590 8.4713
## parent_educhigh school:parent_marital_statusmarried 1.5718 5.9578
## parent_educmaster's degree:parent_marital_statusmarried 2.1560 8.6196
## parent_educsome college:parent_marital_statusmarried -8.3928 5.8669
## parent_educsome high school:parent_marital_statusmarried -7.8355 5.7817
## parent_educbachelor's degree:parent_marital_statussingle -19.7203 9.1319
## parent_educhigh school:parent_marital_statussingle 3.9993 6.5081
## parent_educmaster's degree:parent_marital_statussingle -1.7191 9.2012
## parent_educsome college:parent_marital_statussingle -9.4469 6.5341
## parent_educsome high school:parent_marital_statussingle -9.7176 6.4548
## parent_educbachelor's degree:parent_marital_statuswidowed -38.7612 89.7785
## parent_educhigh school:parent_marital_statuswidowed -117.8054 98.7809
## parent_educmaster's degree:parent_marital_statuswidowed -110.3756 51.7457
## parent_educsome college:parent_marital_statuswidowed -114.0106 64.8797
## parent_educsome high school:parent_marital_statuswidowed -92.5395 77.7614
## parent_educbachelor's degree:practice_sportregularly -3.7294 8.7461
## parent_educhigh school:practice_sportregularly -13.6445 7.5268
## parent_educmaster's degree:practice_sportregularly 0.7016 10.6360
## parent_educsome college:practice_sportregularly -0.2142 7.6542
## parent_educsome high school:practice_sportregularly -2.7852 7.3917
## parent_educbachelor's degree:practice_sportsometimes -12.4201 8.3926
## parent_educhigh school:practice_sportsometimes -13.5033 7.1288
## parent_educmaster's degree:practice_sportsometimes 9.0615 8.8601
## parent_educsome college:practice_sportsometimes 1.2774 7.3663
## parent_educsome high school:practice_sportsometimes 0.4391 6.9262
## parent_educbachelor's degree:is_first_childyes 2.0649 5.1938
## parent_educhigh school:is_first_childyes 8.6134 4.4335
## parent_educmaster's degree:is_first_childyes 6.7664 7.7546
## parent_educsome college:is_first_childyes 9.2132 4.3295
## parent_educsome high school:is_first_childyes 4.6542 4.3602
## parent_educbachelor's degree:transport_meansschool_bus 5.4304 5.1849
## parent_educhigh school:transport_meansschool_bus 4.0937 4.1394
## parent_educmaster's degree:transport_meansschool_bus 11.6831 6.3824
## parent_educsome college:transport_meansschool_bus 4.9041 4.2151
## parent_educsome high school:transport_meansschool_bus 6.9767 4.2890
## parent_educbachelor's degree:wkly_study_hours> 10 -14.7410 7.6498
## parent_educhigh school:wkly_study_hours> 10 -10.1303 6.3679
## parent_educmaster's degree:wkly_study_hours> 10 6.3671 13.7791
## parent_educsome college:wkly_study_hours> 10 -7.2539 6.4097
## parent_educsome high school:wkly_study_hours> 10 -11.3467 6.5283
## parent_educbachelor's degree:wkly_study_hours10-May -3.4329 5.3169
## parent_educhigh school:wkly_study_hours10-May -9.6586 4.9571
## parent_educmaster's degree:wkly_study_hours10-May 0.9849 7.0888
## parent_educsome college:wkly_study_hours10-May -3.5554 5.0476
## parent_educsome high school:wkly_study_hours10-May -10.4143 5.3257
## lunch_typestandard:test_prepnone -1.9452 3.1136
## lunch_typestandard:parent_marital_statusmarried -6.2756 4.0742
## lunch_typestandard:parent_marital_statussingle -2.2019 4.7175
## lunch_typestandard:parent_marital_statuswidowed -21.8879 80.6364
## lunch_typestandard:practice_sportregularly 10.3501 5.3704
## lunch_typestandard:practice_sportsometimes 11.0341 5.1768
## lunch_typestandard:is_first_childyes 0.1283 3.1548
## lunch_typestandard:transport_meansschool_bus -2.5076 2.8951
## lunch_typestandard:wkly_study_hours> 10 5.7376 4.4178
## lunch_typestandard:wkly_study_hours10-May 0.5929 3.3046
## test_prepnone:parent_marital_statusmarried 5.6467 4.1442
## test_prepnone:parent_marital_statussingle 2.5438 4.7712
## test_prepnone:parent_marital_statuswidowed -70.1691 42.1289
## test_prepnone:practice_sportregularly 1.5825 5.1802
## test_prepnone:practice_sportsometimes 3.1630 5.0767
## test_prepnone:is_first_childyes -0.6723 3.1267
## test_prepnone:transport_meansschool_bus 0.4150 2.8429
## test_prepnone:wkly_study_hours> 10 -4.6995 4.4626
## test_prepnone:wkly_study_hours10-May 1.6772 3.5219
## parent_marital_statusmarried:practice_sportregularly 9.1006 6.6592
## parent_marital_statussingle:practice_sportregularly 2.6152 8.7085
## parent_marital_statuswidowed:practice_sportregularly 22.5587 85.2725
## parent_marital_statusmarried:practice_sportsometimes 5.1124 6.5673
## parent_marital_statussingle:practice_sportsometimes -1.6116 8.5136
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -12.7542 4.8986
## parent_marital_statussingle:is_first_childyes -4.9445 5.4292
## parent_marital_statuswidowed:is_first_childyes 47.8196 30.2193
## parent_marital_statusmarried:transport_meansschool_bus 4.6203 4.0454
## parent_marital_statussingle:transport_meansschool_bus -2.0235 4.6103
## parent_marital_statuswidowed:transport_meansschool_bus -34.0699 19.6388
## parent_marital_statusmarried:wkly_study_hours> 10 18.1048 6.3197
## parent_marital_statussingle:wkly_study_hours> 10 21.8022 7.0282
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 1.2179 4.6394
## parent_marital_statussingle:wkly_study_hours10-May 3.3543 5.1241
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -3.3085 6.0157
## practice_sportsometimes:is_first_childyes -5.4272 5.8699
## practice_sportregularly:transport_meansschool_bus 9.9774 5.0267
## practice_sportsometimes:transport_meansschool_bus 5.9885 4.8789
## practice_sportregularly:wkly_study_hours> 10 2.6252 7.1266
## practice_sportsometimes:wkly_study_hours> 10 2.0680 6.9901
## practice_sportregularly:wkly_study_hours10-May 7.8713 5.4844
## practice_sportsometimes:wkly_study_hours10-May 2.5781 5.4074
## is_first_childyes:transport_meansschool_bus -5.3887 3.0599
## is_first_childyes:wkly_study_hours> 10 2.8322 4.6001
## is_first_childyes:wkly_study_hours10-May -4.9634 3.4724
## transport_meansschool_bus:wkly_study_hours> 10 4.0303 4.4205
## transport_meansschool_bus:wkly_study_hours10-May 2.7910 3.1920
## t value Pr(>|t|)
## (Intercept) 3.864 0.000131 ***
## gendermale 0.555 0.578989
## ethnic_groupgroup B -1.327 0.185283
## ethnic_groupgroup C -1.846 0.065599 .
## ethnic_groupgroup D -1.078 0.281775
## ethnic_groupgroup E -0.148 0.882295
## parent_educbachelor's degree 2.111 0.035426 *
## parent_educhigh school 0.934 0.351036
## parent_educmaster's degree -1.156 0.248565
## parent_educsome college -0.260 0.794902
## parent_educsome high school 0.125 0.900238
## lunch_typestandard 0.258 0.796904
## test_prepnone -1.784 0.075183 .
## parent_marital_statusmarried 0.968 0.333510
## parent_marital_statussingle 0.550 0.582326
## parent_marital_statuswidowed 1.344 0.179717
## practice_sportregularly -2.105 0.035959 *
## practice_sportsometimes -1.436 0.151741
## is_first_childyes 1.290 0.197701
## transport_meansschool_bus -0.425 0.671008
## wkly_study_hours> 10 -0.776 0.438299
## wkly_study_hours10-May 0.419 0.675703
## gendermale:ethnic_groupgroup B 0.931 0.352678
## gendermale:ethnic_groupgroup C 1.861 0.063454 .
## gendermale:ethnic_groupgroup D 0.794 0.427811
## gendermale:ethnic_groupgroup E 1.063 0.288659
## gendermale:parent_educbachelor's degree -0.957 0.339269
## gendermale:parent_educhigh school 0.296 0.767289
## gendermale:parent_educmaster's degree 1.656 0.098552 .
## gendermale:parent_educsome college -1.081 0.280453
## gendermale:parent_educsome high school 0.395 0.693115
## gendermale:lunch_typestandard -0.880 0.379317
## gendermale:test_prepnone 0.116 0.907448
## gendermale:parent_marital_statusmarried -0.555 0.579095
## gendermale:parent_marital_statussingle -0.383 0.701904
## gendermale:parent_marital_statuswidowed -0.057 0.954790
## gendermale:practice_sportregularly -0.749 0.454437
## gendermale:practice_sportsometimes -0.751 0.452841
## gendermale:is_first_childyes 0.923 0.356397
## gendermale:transport_meansschool_bus -0.139 0.889859
## gendermale:wkly_study_hours> 10 -0.822 0.411658
## gendermale:wkly_study_hours10-May -0.613 0.540476
## ethnic_groupgroup B:parent_educbachelor's degree -0.319 0.750255
## ethnic_groupgroup C:parent_educbachelor's degree -0.285 0.775863
## ethnic_groupgroup D:parent_educbachelor's degree -0.096 0.923607
## ethnic_groupgroup E:parent_educbachelor's degree -0.660 0.509629
## ethnic_groupgroup B:parent_educhigh school -1.459 0.145350
## ethnic_groupgroup C:parent_educhigh school -0.980 0.327741
## ethnic_groupgroup D:parent_educhigh school -0.508 0.611582
## ethnic_groupgroup E:parent_educhigh school -0.793 0.428002
## ethnic_groupgroup B:parent_educmaster's degree 0.387 0.698911
## ethnic_groupgroup C:parent_educmaster's degree -0.386 0.699808
## ethnic_groupgroup D:parent_educmaster's degree 0.156 0.876431
## ethnic_groupgroup E:parent_educmaster's degree -0.055 0.956503
## ethnic_groupgroup B:parent_educsome college 0.260 0.794732
## ethnic_groupgroup C:parent_educsome college 0.376 0.707455
## ethnic_groupgroup D:parent_educsome college 1.331 0.183836
## ethnic_groupgroup E:parent_educsome college 0.200 0.841866
## ethnic_groupgroup B:parent_educsome high school -1.713 0.087450 .
## ethnic_groupgroup C:parent_educsome high school -0.598 0.550037
## ethnic_groupgroup D:parent_educsome high school -0.133 0.893944
## ethnic_groupgroup E:parent_educsome high school 0.251 0.801944
## ethnic_groupgroup B:lunch_typestandard 0.638 0.523555
## ethnic_groupgroup C:lunch_typestandard 1.394 0.163987
## ethnic_groupgroup D:lunch_typestandard 0.797 0.426112
## ethnic_groupgroup E:lunch_typestandard 0.129 0.897536
## ethnic_groupgroup B:test_prepnone 0.404 0.686423
## ethnic_groupgroup C:test_prepnone 1.377 0.169289
## ethnic_groupgroup D:test_prepnone 1.375 0.169796
## ethnic_groupgroup E:test_prepnone 1.862 0.063307 .
## ethnic_groupgroup B:parent_marital_statusmarried 0.553 0.580679
## ethnic_groupgroup C:parent_marital_statusmarried 0.342 0.732511
## ethnic_groupgroup D:parent_marital_statusmarried -1.160 0.246704
## ethnic_groupgroup E:parent_marital_statusmarried -0.306 0.759941
## ethnic_groupgroup B:parent_marital_statussingle 1.175 0.240572
## ethnic_groupgroup C:parent_marital_statussingle 0.359 0.720004
## ethnic_groupgroup D:parent_marital_statussingle -0.264 0.791728
## ethnic_groupgroup E:parent_marital_statussingle 0.601 0.548513
## ethnic_groupgroup B:parent_marital_statuswidowed 1.041 0.298536
## ethnic_groupgroup C:parent_marital_statuswidowed 1.640 0.101768
## ethnic_groupgroup D:parent_marital_statuswidowed 0.358 0.720446
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.682 0.093341 .
## ethnic_groupgroup C:practice_sportregularly 1.461 0.144908
## ethnic_groupgroup D:practice_sportregularly 1.315 0.189183
## ethnic_groupgroup E:practice_sportregularly 1.483 0.138959
## ethnic_groupgroup B:practice_sportsometimes 1.066 0.287304
## ethnic_groupgroup C:practice_sportsometimes 1.687 0.092504 .
## ethnic_groupgroup D:practice_sportsometimes 1.040 0.299174
## ethnic_groupgroup E:practice_sportsometimes 1.011 0.312443
## ethnic_groupgroup B:is_first_childyes 1.706 0.088779 .
## ethnic_groupgroup C:is_first_childyes -0.032 0.974411
## ethnic_groupgroup D:is_first_childyes 0.199 0.842418
## ethnic_groupgroup E:is_first_childyes 0.543 0.587200
## ethnic_groupgroup B:transport_meansschool_bus -0.684 0.494241
## ethnic_groupgroup C:transport_meansschool_bus -1.837 0.066921 .
## ethnic_groupgroup D:transport_meansschool_bus -0.539 0.590297
## ethnic_groupgroup E:transport_meansschool_bus -1.804 0.072093 .
## ethnic_groupgroup B:wkly_study_hours> 10 -0.984 0.325710
## ethnic_groupgroup C:wkly_study_hours> 10 0.140 0.888562
## ethnic_groupgroup D:wkly_study_hours> 10 0.416 0.678007
## ethnic_groupgroup E:wkly_study_hours> 10 -0.319 0.749646
## ethnic_groupgroup B:wkly_study_hours10-May -0.698 0.485813
## ethnic_groupgroup C:wkly_study_hours10-May 0.286 0.775035
## ethnic_groupgroup D:wkly_study_hours10-May 0.301 0.763685
## ethnic_groupgroup E:wkly_study_hours10-May -0.290 0.772121
## parent_educbachelor's degree:lunch_typestandard 0.411 0.681330
## parent_educhigh school:lunch_typestandard 0.089 0.929339
## parent_educmaster's degree:lunch_typestandard 1.305 0.192749
## parent_educsome college:lunch_typestandard 0.790 0.430256
## parent_educsome high school:lunch_typestandard 1.277 0.202472
## parent_educbachelor's degree:test_prepnone -0.839 0.401869
## parent_educhigh school:test_prepnone -0.260 0.794920
## parent_educmaster's degree:test_prepnone -0.225 0.822173
## parent_educsome college:test_prepnone -0.552 0.581102
## parent_educsome high school:test_prepnone 0.731 0.465380
## parent_educbachelor's degree:parent_marital_statusmarried -2.096 0.036705 *
## parent_educhigh school:parent_marital_statusmarried 0.264 0.792052
## parent_educmaster's degree:parent_marital_statusmarried 0.250 0.802627
## parent_educsome college:parent_marital_statusmarried -1.431 0.153379
## parent_educsome high school:parent_marital_statusmarried -1.355 0.176143
## parent_educbachelor's degree:parent_marital_statussingle -2.160 0.031431 *
## parent_educhigh school:parent_marital_statussingle 0.615 0.539246
## parent_educmaster's degree:parent_marital_statussingle -0.187 0.851886
## parent_educsome college:parent_marital_statussingle -1.446 0.149058
## parent_educsome high school:parent_marital_statussingle -1.505 0.133023
## parent_educbachelor's degree:parent_marital_statuswidowed -0.432 0.666171
## parent_educhigh school:parent_marital_statuswidowed -1.193 0.233767
## parent_educmaster's degree:parent_marital_statuswidowed -2.133 0.033557 *
## parent_educsome college:parent_marital_statuswidowed -1.757 0.079672 .
## parent_educsome high school:parent_marital_statuswidowed -1.190 0.234766
## parent_educbachelor's degree:practice_sportregularly -0.426 0.670053
## parent_educhigh school:practice_sportregularly -1.813 0.070647 .
## parent_educmaster's degree:practice_sportregularly 0.066 0.947437
## parent_educsome college:practice_sportregularly -0.028 0.977692
## parent_educsome high school:practice_sportregularly -0.377 0.706532
## parent_educbachelor's degree:practice_sportsometimes -1.480 0.139724
## parent_educhigh school:practice_sportsometimes -1.894 0.058951 .
## parent_educmaster's degree:practice_sportsometimes 1.023 0.307081
## parent_educsome college:practice_sportsometimes 0.173 0.862420
## parent_educsome high school:practice_sportsometimes 0.063 0.949489
## parent_educbachelor's degree:is_first_childyes 0.398 0.691162
## parent_educhigh school:is_first_childyes 1.943 0.052773 .
## parent_educmaster's degree:is_first_childyes 0.873 0.383445
## parent_educsome college:is_first_childyes 2.128 0.033972 *
## parent_educsome high school:is_first_childyes 1.067 0.286450
## parent_educbachelor's degree:transport_meansschool_bus 1.047 0.295600
## parent_educhigh school:transport_meansschool_bus 0.989 0.323307
## parent_educmaster's degree:transport_meansschool_bus 1.831 0.067950 .
## parent_educsome college:transport_meansschool_bus 1.163 0.245371
## parent_educsome high school:transport_meansschool_bus 1.627 0.104635
## parent_educbachelor's degree:wkly_study_hours> 10 -1.927 0.054721 .
## parent_educhigh school:wkly_study_hours> 10 -1.591 0.112471
## parent_educmaster's degree:wkly_study_hours> 10 0.462 0.644281
## parent_educsome college:wkly_study_hours> 10 -1.132 0.258463
## parent_educsome high school:wkly_study_hours> 10 -1.738 0.083002 .
## parent_educbachelor's degree:wkly_study_hours10-May -0.646 0.518891
## parent_educhigh school:wkly_study_hours10-May -1.948 0.052093 .
## parent_educmaster's degree:wkly_study_hours10-May 0.139 0.889578
## parent_educsome college:wkly_study_hours10-May -0.704 0.481637
## parent_educsome high school:wkly_study_hours10-May -1.955 0.051251 .
## lunch_typestandard:test_prepnone -0.625 0.532521
## lunch_typestandard:parent_marital_statusmarried -1.540 0.124305
## lunch_typestandard:parent_marital_statussingle -0.467 0.640946
## lunch_typestandard:parent_marital_statuswidowed -0.271 0.786200
## lunch_typestandard:practice_sportregularly 1.927 0.054686 .
## lunch_typestandard:practice_sportsometimes 2.131 0.033689 *
## lunch_typestandard:is_first_childyes 0.041 0.967588
## lunch_typestandard:transport_meansschool_bus -0.866 0.386933
## lunch_typestandard:wkly_study_hours> 10 1.299 0.194815
## lunch_typestandard:wkly_study_hours10-May 0.179 0.857717
## test_prepnone:parent_marital_statusmarried 1.363 0.173819
## test_prepnone:parent_marital_statussingle 0.533 0.594231
## test_prepnone:parent_marital_statuswidowed -1.666 0.096615 .
## test_prepnone:practice_sportregularly 0.305 0.760155
## test_prepnone:practice_sportsometimes 0.623 0.533633
## test_prepnone:is_first_childyes -0.215 0.829855
## test_prepnone:transport_meansschool_bus 0.146 0.884028
## test_prepnone:wkly_study_hours> 10 -1.053 0.292966
## test_prepnone:wkly_study_hours10-May 0.476 0.634185
## parent_marital_statusmarried:practice_sportregularly 1.367 0.172546
## parent_marital_statussingle:practice_sportregularly 0.300 0.764107
## parent_marital_statuswidowed:practice_sportregularly 0.265 0.791500
## parent_marital_statusmarried:practice_sportsometimes 0.778 0.436770
## parent_marital_statussingle:practice_sportsometimes -0.189 0.849955
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -2.604 0.009583 **
## parent_marital_statussingle:is_first_childyes -0.911 0.363014
## parent_marital_statuswidowed:is_first_childyes 1.582 0.114379
## parent_marital_statusmarried:transport_meansschool_bus 1.142 0.254126
## parent_marital_statussingle:transport_meansschool_bus -0.439 0.660982
## parent_marital_statuswidowed:transport_meansschool_bus -1.735 0.083576 .
## parent_marital_statusmarried:wkly_study_hours> 10 2.865 0.004403 **
## parent_marital_statussingle:wkly_study_hours> 10 3.102 0.002064 **
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 0.263 0.793062
## parent_marital_statussingle:wkly_study_hours10-May 0.655 0.513103
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -0.550 0.582650
## practice_sportsometimes:is_first_childyes -0.925 0.355759
## practice_sportregularly:transport_meansschool_bus 1.985 0.047872 *
## practice_sportsometimes:transport_meansschool_bus 1.227 0.220411
## practice_sportregularly:wkly_study_hours> 10 0.368 0.712800
## practice_sportsometimes:wkly_study_hours> 10 0.296 0.767511
## practice_sportregularly:wkly_study_hours10-May 1.435 0.152043
## practice_sportsometimes:wkly_study_hours10-May 0.477 0.633796
## is_first_childyes:transport_meansschool_bus -1.761 0.079028 .
## is_first_childyes:wkly_study_hours> 10 0.616 0.538468
## is_first_childyes:wkly_study_hours10-May -1.429 0.153714
## transport_meansschool_bus:wkly_study_hours> 10 0.912 0.362481
## transport_meansschool_bus:wkly_study_hours10-May 0.874 0.382459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.21 on 383 degrees of freedom
## Multiple R-squared: 0.5635, Adjusted R-squared: 0.3287
## F-statistic: 2.4 on 206 and 383 DF, p-value: 7.833e-14stepwise_model_math <- step(full_fit_math, direction = "both", trace = 1)## Start: AIC=3204.25
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3316.3 70110 3192.8
## - parent_educ:test_prep 5 440.1 67234 3198.1
## - gender:parent_marital_status 3 54.0 66847 3198.7
## - parent_educ:lunch_type 5 591.2 67385 3199.4
## - ethnic_group:wkly_study_hours 8 1323.8 68117 3199.8
## - parent_educ:wkly_study_hours 10 1801.1 68595 3199.9
## - test_prep:practice_sport 2 93.5 66887 3201.1
## - parent_marital_status:practice_sport 4 550.9 67344 3201.1
## - gender:practice_sport 2 107.4 66901 3201.2
## - gender:wkly_study_hours 2 123.6 66917 3201.3
## - parent_educ:transport_means 5 809.3 67603 3201.4
## - ethnic_group:lunch_type 4 591.0 67384 3201.4
## - transport_means:wkly_study_hours 2 187.6 66981 3201.9
## - practice_sport:is_first_child 2 198.4 66992 3202.0
## - lunch_type:is_first_child 1 0.3 66794 3202.3
## - gender:test_prep 1 2.4 66796 3202.3
## - gender:transport_means 1 3.3 66797 3202.3
## - test_prep:transport_means 1 3.7 66797 3202.3
## - test_prep:is_first_child 1 8.1 66802 3202.3
## - practice_sport:wkly_study_hours 4 718.0 67511 3202.6
## - lunch_type:test_prep 1 68.1 66862 3202.9
## - ethnic_group:practice_sport 8 1701.9 68495 3203.1
## - lunch_type:wkly_study_hours 2 352.3 67146 3203.4
## - lunch_type:transport_means 1 130.8 66924 3203.4
## - gender:lunch_type 1 135.1 66929 3203.4
## - gender:is_first_child 1 148.7 66942 3203.6
## - test_prep:parent_marital_status 2 403.4 67197 3203.8
## - gender:ethnic_group 4 869.6 67663 3203.9
## - parent_educ:is_first_child 5 1132.1 67926 3204.2
## <none> 66793 3204.3
## - gender:parent_educ 5 1173.5 67967 3204.5
## - test_prep:wkly_study_hours 2 516.4 67310 3204.8
## - ethnic_group:parent_marital_status 9 2150.3 68944 3204.9
## - lunch_type:parent_marital_status 2 552.7 67346 3205.1
## - ethnic_group:test_prep 4 1027.0 67820 3205.3
## - parent_educ:practice_sport 10 2545.2 69339 3206.3
## - ethnic_group:is_first_child 4 1194.4 67988 3206.7
## - parent_educ:parent_marital_status 13 3334.3 70128 3207.0
## - is_first_child:transport_means 1 540.9 67334 3207.0
## - practice_sport:transport_means 2 773.2 67567 3207.0
## - is_first_child:wkly_study_hours 2 781.2 67575 3207.1
## - lunch_type:practice_sport 2 806.9 67600 3207.3
## - ethnic_group:transport_means 4 1369.9 68163 3208.2
## - parent_marital_status:transport_means 3 1399.6 68193 3210.5
## - parent_marital_status:wkly_study_hours 4 2104.0 68897 3214.5
## - parent_marital_status:is_first_child 2 1736.9 68530 3215.4
##
## Step: AIC=3192.84
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1343.3 71453 3184.0
## - ethnic_group:wkly_study_hours 8 963.6 71073 3184.9
## - parent_educ:test_prep 5 338.0 70448 3185.7
## - parent_educ:lunch_type 5 451.8 70562 3186.6
## - gender:parent_marital_status 3 77.7 70187 3187.5
## - ethnic_group:practice_sport 8 1396.5 71506 3188.5
## - parent_marital_status:practice_sport 4 526.1 70636 3189.3
## - gender:wkly_study_hours 2 84.8 70194 3189.6
## - test_prep:practice_sport 2 90.5 70200 3189.6
## - parent_educ:transport_means 5 905.7 71015 3190.4
## - practice_sport:is_first_child 2 203.1 70313 3190.5
## - ethnic_group:lunch_type 4 690.5 70800 3190.6
## - gender:practice_sport 2 238.2 70348 3190.8
## - lunch_type:is_first_child 1 0.2 70110 3190.8
## - gender:transport_means 1 0.2 70110 3190.8
## - lunch_type:test_prep 1 1.0 70111 3190.8
## - gender:test_prep 1 6.0 70116 3190.9
## - test_prep:transport_means 1 13.7 70123 3191.0
## - gender:is_first_child 1 26.2 70136 3191.1
## - test_prep:is_first_child 1 33.4 70143 3191.1
## - lunch_type:parent_marital_status 2 291.9 70402 3191.3
## - gender:lunch_type 1 114.9 70225 3191.8
## - ethnic_group:test_prep 4 836.4 70946 3191.8
## - transport_means:wkly_study_hours 2 360.6 70470 3191.9
## - practice_sport:wkly_study_hours 4 853.3 70963 3192.0
## - parent_educ:is_first_child 5 1098.4 71208 3192.0
## - gender:ethnic_group 4 860.5 70970 3192.0
## - test_prep:parent_marital_status 2 402.3 70512 3192.2
## - gender:parent_educ 5 1125.5 71235 3192.2
## - lunch_type:transport_means 1 226.0 70336 3192.7
## <none> 70110 3192.8
## - lunch_type:wkly_study_hours 2 538.0 70648 3193.3
## - is_first_child:wkly_study_hours 2 543.0 70653 3193.4
## - test_prep:wkly_study_hours 2 569.9 70680 3193.6
## - ethnic_group:parent_marital_status 9 2293.6 72403 3193.8
## - parent_educ:practice_sport 10 2568.4 72678 3194.1
## - is_first_child:transport_means 1 470.4 70580 3194.8
## - practice_sport:transport_means 2 724.0 70834 3194.9
## - lunch_type:practice_sport 2 860.0 70970 3196.0
## - ethnic_group:transport_means 4 1409.3 71519 3196.6
## - parent_marital_status:transport_means 3 1169.4 71279 3196.6
## - ethnic_group:is_first_child 4 1483.9 71594 3197.2
## - parent_marital_status:wkly_study_hours 4 1669.0 71779 3198.7
## - parent_educ:parent_marital_status 13 3948.0 74058 3199.2
## - parent_marital_status:is_first_child 2 1642.9 71753 3202.5
## + ethnic_group:parent_educ 20 3316.3 66793 3204.3
##
## Step: AIC=3184.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 1060.7 72514 3176.7
## - parent_educ:lunch_type 5 330.0 71783 3176.8
## - parent_educ:test_prep 5 395.5 71848 3177.3
## - gender:parent_marital_status 3 71.4 71524 3178.6
## - ethnic_group:practice_sport 8 1299.7 72753 3178.7
## - ethnic_group:lunch_type 4 543.5 71997 3180.5
## - parent_marital_status:practice_sport 4 607.7 72061 3181.0
## - test_prep:practice_sport 2 164.8 71618 3181.4
## - gender:wkly_study_hours 2 178.6 71632 3181.5
## - gender:practice_sport 2 193.6 71647 3181.6
## - practice_sport:is_first_child 2 204.1 71657 3181.7
## - parent_educ:transport_means 5 939.1 72392 3181.7
## - practice_sport:wkly_study_hours 4 701.9 72155 3181.8
## - lunch_type:test_prep 1 0.1 71453 3182.0
## - gender:transport_means 1 2.0 71455 3182.1
## - lunch_type:is_first_child 1 7.3 71460 3182.1
## - gender:test_prep 1 9.7 71463 3182.1
## - ethnic_group:test_prep 4 740.2 72193 3182.1
## - test_prep:is_first_child 1 16.6 71470 3182.2
## - test_prep:transport_means 1 16.8 71470 3182.2
## - gender:is_first_child 1 23.1 71476 3182.2
## - lunch_type:parent_marital_status 2 307.7 71761 3182.6
## - lunch_type:wkly_study_hours 2 327.7 71781 3182.7
## - gender:lunch_type 1 94.3 71547 3182.8
## - gender:parent_educ 5 1100.3 72553 3183.1
## - transport_means:wkly_study_hours 2 407.0 71860 3183.4
## - parent_educ:is_first_child 5 1144.4 72597 3183.4
## - is_first_child:wkly_study_hours 2 417.3 71870 3183.5
## - gender:ethnic_group 4 920.2 72373 3183.6
## - test_prep:parent_marital_status 2 440.7 71894 3183.7
## <none> 71453 3184.0
## - lunch_type:transport_means 1 318.5 71772 3184.7
## - practice_sport:transport_means 2 638.5 72091 3185.3
## - is_first_child:transport_means 1 494.4 71947 3186.1
## - ethnic_group:parent_marital_status 9 2511.3 73964 3186.4
## - ethnic_group:transport_means 4 1268.3 72721 3186.4
## - lunch_type:practice_sport 2 795.8 72249 3186.6
## - test_prep:wkly_study_hours 2 800.9 72254 3186.6
## - parent_educ:practice_sport 10 2798.9 74252 3186.7
## - parent_marital_status:transport_means 3 1242.1 72695 3188.2
## - ethnic_group:is_first_child 4 1585.3 73038 3189.0
## - parent_marital_status:wkly_study_hours 4 1707.0 73160 3190.0
## - parent_educ:parent_marital_status 13 4246.1 75699 3192.1
## + parent_educ:wkly_study_hours 10 1343.3 70110 3192.8
## - parent_marital_status:is_first_child 2 1880.9 73334 3195.4
## + ethnic_group:parent_educ 20 2858.5 68595 3199.9
##
## Step: AIC=3176.73
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 294.6 72808 3169.1
## - parent_educ:test_prep 5 425.1 72939 3170.2
## - gender:parent_marital_status 3 77.7 72591 3171.4
## - ethnic_group:practice_sport 8 1324.8 73838 3171.4
## - parent_marital_status:practice_sport 4 477.7 72991 3172.6
## - ethnic_group:lunch_type 4 592.3 73106 3173.5
## - parent_educ:transport_means 5 852.7 73366 3173.6
## - gender:wkly_study_hours 2 138.0 72652 3173.9
## - test_prep:practice_sport 2 157.5 72671 3174.0
## - ethnic_group:test_prep 4 699.6 73213 3174.4
## - gender:practice_sport 2 212.8 72726 3174.5
## - practice_sport:wkly_study_hours 4 715.7 73229 3174.5
## - practice_sport:is_first_child 2 230.8 72744 3174.6
## - lunch_type:test_prep 1 3.8 72518 3174.8
## - gender:transport_means 1 3.8 72518 3174.8
## - transport_means:wkly_study_hours 2 251.7 72765 3174.8
## - gender:is_first_child 1 9.8 72523 3174.8
## - lunch_type:is_first_child 1 10.0 72524 3174.8
## - test_prep:transport_means 1 14.0 72528 3174.8
## - gender:test_prep 1 32.5 72546 3175.0
## - test_prep:is_first_child 1 49.0 72563 3175.1
## - gender:parent_educ 5 1062.9 73577 3175.3
## - lunch_type:parent_marital_status 2 327.1 72841 3175.4
## - gender:lunch_type 1 100.0 72614 3175.5
## - lunch_type:wkly_study_hours 2 408.7 72922 3176.0
## - gender:ethnic_group 4 915.4 73429 3176.1
## - parent_educ:is_first_child 5 1198.1 73712 3176.4
## <none> 72514 3176.7
## - test_prep:parent_marital_status 2 499.2 73013 3176.8
## - is_first_child:wkly_study_hours 2 516.9 73031 3176.9
## - lunch_type:transport_means 1 292.6 72806 3177.1
## - ethnic_group:parent_marital_status 9 2400.6 74914 3177.9
## - practice_sport:transport_means 2 658.8 73173 3178.1
## - ethnic_group:transport_means 4 1211.0 73725 3178.5
## - parent_educ:practice_sport 10 2730.9 75245 3178.5
## - is_first_child:transport_means 1 494.6 73008 3178.7
## - test_prep:wkly_study_hours 2 797.9 73312 3179.2
## - lunch_type:practice_sport 2 872.4 73386 3179.8
## - parent_marital_status:transport_means 3 1276.5 73790 3181.0
## - parent_marital_status:wkly_study_hours 4 1550.3 74064 3181.2
## - ethnic_group:is_first_child 4 1638.0 74152 3181.9
## - parent_educ:parent_marital_status 13 4105.1 76619 3183.2
## + ethnic_group:wkly_study_hours 8 1060.7 71453 3184.0
## + parent_educ:wkly_study_hours 10 1440.4 71073 3184.9
## - parent_marital_status:is_first_child 2 1784.1 74298 3187.1
## + ethnic_group:parent_educ 20 2546.0 69968 3195.6
##
## Step: AIC=3169.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 359.4 73168 3162.0
## - ethnic_group:practice_sport 8 1287.1 74095 3163.5
## - gender:parent_marital_status 3 84.3 72893 3163.8
## - parent_marital_status:practice_sport 4 510.3 73319 3165.2
## - ethnic_group:lunch_type 4 611.1 73419 3166.1
## - gender:wkly_study_hours 2 132.3 72941 3166.2
## - test_prep:practice_sport 2 157.8 72966 3166.4
## - parent_educ:transport_means 5 914.4 73723 3166.5
## - ethnic_group:test_prep 4 686.0 73494 3166.7
## - gender:practice_sport 2 217.7 73026 3166.9
## - practice_sport:is_first_child 2 246.8 73055 3167.1
## - gender:transport_means 1 1.0 72809 3167.1
## - lunch_type:test_prep 1 1.8 72810 3167.1
## - test_prep:transport_means 1 14.7 72823 3167.2
## - lunch_type:is_first_child 1 14.9 72823 3167.2
## - practice_sport:wkly_study_hours 4 759.8 73568 3167.2
## - transport_means:wkly_study_hours 2 270.4 73079 3167.3
## - gender:is_first_child 1 30.9 72839 3167.4
## - gender:test_prep 1 38.9 72847 3167.4
## - test_prep:is_first_child 1 39.2 72847 3167.4
## - gender:parent_educ 5 1056.1 73864 3167.6
## - lunch_type:parent_marital_status 2 329.5 73138 3167.8
## - lunch_type:wkly_study_hours 2 370.3 73179 3168.1
## - gender:lunch_type 1 140.8 72949 3168.3
## - gender:ethnic_group 4 914.4 73723 3168.5
## - parent_educ:is_first_child 5 1171.9 73980 3168.5
## <none> 72808 3169.1
## - test_prep:parent_marital_status 2 532.2 73340 3169.4
## - lunch_type:transport_means 1 287.4 73096 3169.4
## - is_first_child:wkly_study_hours 2 545.4 73354 3169.5
## - ethnic_group:parent_marital_status 9 2363.0 75171 3170.0
## - ethnic_group:transport_means 4 1190.2 73998 3170.7
## - practice_sport:transport_means 2 751.2 73559 3171.2
## - is_first_child:transport_means 1 510.9 73319 3171.2
## - test_prep:wkly_study_hours 2 786.4 73595 3171.5
## - lunch_type:practice_sport 2 835.6 73644 3171.9
## - parent_educ:practice_sport 10 2882.8 75691 3172.0
## - parent_marital_status:transport_means 3 1345.6 74154 3173.9
## - ethnic_group:is_first_child 4 1656.4 74465 3174.4
## - parent_marital_status:wkly_study_hours 4 1675.9 74484 3174.5
## - parent_educ:parent_marital_status 13 4184.5 76993 3176.1
## + parent_educ:lunch_type 5 294.6 72514 3176.7
## + ethnic_group:wkly_study_hours 8 1025.2 71783 3176.8
## + parent_educ:wkly_study_hours 10 1298.6 71510 3178.5
## - parent_marital_status:is_first_child 2 1962.0 74770 3180.8
## + ethnic_group:parent_educ 20 2526.6 70282 3188.3
##
## Step: AIC=3162.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1278.6 74446 3156.2
## - gender:parent_marital_status 3 87.6 73255 3156.7
## - parent_marital_status:practice_sport 4 490.9 73659 3158.0
## - ethnic_group:test_prep 4 630.4 73798 3159.1
## - test_prep:practice_sport 2 132.4 73300 3159.1
## - gender:wkly_study_hours 2 150.1 73318 3159.2
## - ethnic_group:lunch_type 4 667.4 73835 3159.4
## - parent_educ:transport_means 5 964.9 74132 3159.8
## - gender:practice_sport 2 214.9 73382 3159.8
## - gender:transport_means 1 0.1 73168 3160.0
## - gender:parent_educ 5 1000.6 74168 3160.0
## - practice_sport:wkly_study_hours 4 751.8 73919 3160.1
## - lunch_type:test_prep 1 7.1 73175 3160.1
## - test_prep:transport_means 1 12.8 73180 3160.1
## - transport_means:wkly_study_hours 2 262.3 73430 3160.1
## - lunch_type:is_first_child 1 24.2 73192 3160.2
## - gender:is_first_child 1 25.1 73193 3160.2
## - practice_sport:is_first_child 2 277.1 73445 3160.3
## - test_prep:is_first_child 1 46.8 73214 3160.4
## - gender:test_prep 1 47.0 73215 3160.4
## - lunch_type:parent_marital_status 2 304.2 73472 3160.5
## - gender:lunch_type 1 121.5 73289 3161.0
## - lunch_type:wkly_study_hours 2 410.5 73578 3161.3
## - gender:ethnic_group 4 912.8 74080 3161.3
## - parent_educ:is_first_child 5 1196.4 74364 3161.6
## - is_first_child:wkly_study_hours 2 486.7 73654 3161.9
## <none> 73168 3162.0
## - lunch_type:transport_means 1 256.3 73424 3162.1
## - test_prep:parent_marital_status 2 519.3 73687 3162.2
## - ethnic_group:parent_marital_status 9 2307.6 75475 3162.3
## - ethnic_group:transport_means 4 1145.8 74313 3163.2
## - practice_sport:transport_means 2 780.1 73948 3164.3
## - parent_educ:practice_sport 10 2851.5 76019 3164.6
## - is_first_child:transport_means 1 590.4 73758 3164.8
## - test_prep:wkly_study_hours 2 856.9 74024 3164.9
## - lunch_type:practice_sport 2 894.2 74062 3165.2
## - parent_marital_status:transport_means 3 1347.2 74515 3166.8
## - parent_marital_status:wkly_study_hours 4 1749.0 74917 3168.0
## - ethnic_group:is_first_child 4 1750.8 74918 3168.0
## - parent_educ:parent_marital_status 13 4071.8 77239 3168.0
## + parent_educ:test_prep 5 359.4 72808 3169.1
## + ethnic_group:wkly_study_hours 8 1054.8 72113 3169.5
## + parent_educ:lunch_type 5 228.9 72939 3170.2
## + parent_educ:wkly_study_hours 10 1351.3 71816 3171.0
## - parent_marital_status:is_first_child 2 2006.6 75174 3174.0
## + ethnic_group:parent_educ 20 2379.5 70788 3182.5
##
## Step: AIC=3156.25
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 67.0 74513 3150.8
## - parent_educ:transport_means 5 841.7 75288 3152.9
## - test_prep:practice_sport 2 106.9 74553 3153.1
## - ethnic_group:test_prep 4 620.2 75066 3153.1
## - gender:parent_educ 5 928.1 75374 3153.6
## - parent_marital_status:practice_sport 4 715.9 75162 3153.9
## - gender:ethnic_group 4 740.0 75186 3154.1
## - practice_sport:is_first_child 2 233.2 74679 3154.1
## - gender:wkly_study_hours 2 239.5 74686 3154.1
## - ethnic_group:lunch_type 4 753.4 75200 3154.2
## - practice_sport:wkly_study_hours 4 757.6 75204 3154.2
## - gender:transport_means 1 0.0 74446 3154.2
## - gender:is_first_child 1 4.0 74450 3154.3
## - lunch_type:is_first_child 1 6.3 74452 3154.3
## - test_prep:transport_means 1 14.3 74461 3154.4
## - gender:test_prep 1 27.0 74473 3154.5
## - test_prep:is_first_child 1 36.1 74482 3154.5
## - lunch_type:test_prep 1 40.4 74487 3154.6
## - transport_means:wkly_study_hours 2 312.2 74758 3154.7
## - lunch_type:parent_marital_status 2 336.7 74783 3154.9
## - gender:lunch_type 1 91.8 74538 3155.0
## - gender:practice_sport 2 372.3 74818 3155.2
## - lunch_type:wkly_study_hours 2 438.7 74885 3155.7
## - lunch_type:transport_means 1 207.5 74654 3155.9
## <none> 74446 3156.2
## - is_first_child:wkly_study_hours 2 513.1 74959 3156.3
## - test_prep:parent_marital_status 2 564.5 75011 3156.7
## - ethnic_group:parent_marital_status 9 2399.2 76845 3157.0
## - parent_educ:is_first_child 5 1373.5 75820 3157.0
## - test_prep:wkly_study_hours 2 686.9 75133 3157.7
## - ethnic_group:transport_means 4 1209.0 75655 3157.8
## - practice_sport:transport_means 2 767.5 75214 3158.3
## - lunch_type:practice_sport 2 901.2 75347 3159.3
## - parent_educ:practice_sport 10 2985.5 77432 3159.4
## - is_first_child:transport_means 1 699.2 75145 3159.8
## - ethnic_group:is_first_child 4 1570.1 76016 3160.6
## - parent_educ:parent_marital_status 13 4000.5 78447 3161.1
## - parent_marital_status:transport_means 3 1482.2 75928 3161.9
## + ethnic_group:practice_sport 8 1278.6 73168 3162.0
## - parent_marital_status:wkly_study_hours 4 1838.7 76285 3162.6
## + parent_educ:test_prep 5 350.9 74095 3163.5
## + ethnic_group:wkly_study_hours 8 1066.6 73380 3163.7
## + parent_educ:lunch_type 5 190.6 74256 3164.7
## + parent_educ:wkly_study_hours 10 1298.4 73148 3165.9
## - parent_marital_status:is_first_child 2 1757.2 76203 3166.0
## + ethnic_group:parent_educ 20 2053.9 72392 3179.7
##
## Step: AIC=3150.78
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 837.2 75350 3147.4
## - test_prep:practice_sport 2 123.5 74637 3147.8
## - ethnic_group:test_prep 4 647.9 75161 3147.9
## - gender:parent_educ 5 953.7 75467 3148.3
## - parent_marital_status:practice_sport 4 707.6 75221 3148.4
## - gender:ethnic_group 4 713.3 75227 3148.4
## - practice_sport:is_first_child 2 226.7 74740 3148.6
## - gender:transport_means 1 0.1 74513 3148.8
## - ethnic_group:lunch_type 4 763.7 75277 3148.8
## - lunch_type:is_first_child 1 5.5 74519 3148.8
## - gender:wkly_study_hours 2 259.9 74773 3148.8
## - gender:is_first_child 1 7.7 74521 3148.8
## - test_prep:transport_means 1 13.5 74527 3148.9
## - practice_sport:wkly_study_hours 4 781.9 75295 3148.9
## - gender:test_prep 1 30.2 74543 3149.0
## - test_prep:is_first_child 1 37.1 74550 3149.1
## - lunch_type:test_prep 1 38.2 74551 3149.1
## - transport_means:wkly_study_hours 2 313.8 74827 3149.3
## - gender:lunch_type 1 86.4 74600 3149.5
## - lunch_type:parent_marital_status 2 372.7 74886 3149.7
## - gender:practice_sport 2 398.1 74911 3149.9
## - lunch_type:wkly_study_hours 2 465.2 74978 3150.5
## - lunch_type:transport_means 1 219.7 74733 3150.5
## - is_first_child:wkly_study_hours 2 502.1 75015 3150.7
## <none> 74513 3150.8
## - test_prep:parent_marital_status 2 572.4 75086 3151.3
## - parent_educ:is_first_child 5 1383.9 75897 3151.6
## - test_prep:wkly_study_hours 2 682.1 75195 3152.2
## - ethnic_group:transport_means 4 1201.4 75715 3152.2
## - practice_sport:transport_means 2 757.6 75271 3152.7
## - ethnic_group:parent_marital_status 9 2645.4 77159 3153.4
## - lunch_type:practice_sport 2 979.2 75492 3154.5
## - parent_educ:practice_sport 10 3086.3 77599 3154.7
## - is_first_child:transport_means 1 756.1 75269 3154.7
## - ethnic_group:is_first_child 4 1552.8 76066 3154.9
## - parent_educ:parent_marital_status 13 3992.8 78506 3155.6
## + gender:parent_marital_status 3 67.0 74446 3156.2
## + ethnic_group:practice_sport 8 1258.0 73255 3156.7
## - parent_marital_status:wkly_study_hours 4 1820.1 76333 3157.0
## - parent_marital_status:transport_means 3 1677.8 76191 3157.9
## + parent_educ:test_prep 5 353.8 74159 3158.0
## + ethnic_group:wkly_study_hours 8 1069.4 73444 3158.3
## + parent_educ:lunch_type 5 197.6 74316 3159.2
## + parent_educ:wkly_study_hours 10 1285.8 73227 3160.5
## - parent_marital_status:is_first_child 2 1819.2 76332 3161.0
## + ethnic_group:parent_educ 20 2094.0 72419 3174.0
##
## Step: AIC=3147.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 625.0 75975 3144.2
## - parent_marital_status:practice_sport 4 639.9 75990 3144.4
## - test_prep:practice_sport 2 137.2 75488 3144.4
## - practice_sport:is_first_child 2 183.7 75534 3144.8
## - ethnic_group:test_prep 4 699.4 76050 3144.8
## - gender:parent_educ 5 964.7 76315 3144.9
## - gender:wkly_study_hours 2 223.3 75574 3145.1
## - gender:transport_means 1 0.0 75350 3145.4
## - lunch_type:is_first_child 1 3.2 75354 3145.4
## - gender:is_first_child 1 3.4 75354 3145.4
## - test_prep:transport_means 1 18.3 75369 3145.5
## - gender:test_prep 1 25.6 75376 3145.6
## - transport_means:wkly_study_hours 2 288.2 75639 3145.6
## - lunch_type:test_prep 1 45.2 75396 3145.7
## - test_prep:is_first_child 1 70.8 75421 3145.9
## - practice_sport:wkly_study_hours 4 851.2 76202 3146.0
## - gender:lunch_type 1 110.4 75461 3146.2
## - ethnic_group:lunch_type 4 903.0 76253 3146.4
## - lunch_type:parent_marital_status 2 449.3 75800 3146.9
## - is_first_child:wkly_study_hours 2 475.6 75826 3147.1
## - lunch_type:transport_means 1 226.7 75577 3147.1
## - gender:practice_sport 2 488.4 75839 3147.2
## <none> 75350 3147.4
## - test_prep:parent_marital_status 2 561.5 75912 3147.8
## - lunch_type:wkly_study_hours 2 588.6 75939 3148.0
## - practice_sport:transport_means 2 593.3 75944 3148.0
## - parent_educ:is_first_child 5 1426.3 76777 3148.4
## - test_prep:wkly_study_hours 2 674.7 76025 3148.6
## - ethnic_group:transport_means 4 1321.3 76672 3149.6
## - ethnic_group:parent_marital_status 9 2697.0 78047 3150.1
## - parent_educ:practice_sport 10 3037.1 78388 3150.7
## - is_first_child:transport_means 1 689.2 76040 3150.7
## + parent_educ:transport_means 5 837.2 74513 3150.8
## - ethnic_group:is_first_child 4 1647.5 76998 3152.1
## - lunch_type:practice_sport 2 1148.9 76499 3152.3
## - parent_educ:parent_marital_status 13 4056.5 79407 3152.3
## + gender:parent_marital_status 3 62.5 75288 3152.9
## - parent_marital_status:transport_means 3 1562.5 76913 3153.5
## - parent_marital_status:wkly_study_hours 4 1918.6 77269 3154.2
## + parent_educ:test_prep 5 390.5 74960 3154.3
## + ethnic_group:practice_sport 8 1138.4 74212 3154.4
## + parent_educ:lunch_type 5 246.2 75104 3155.4
## + ethnic_group:wkly_study_hours 8 977.8 74373 3155.7
## - parent_marital_status:is_first_child 2 1802.2 77153 3157.3
## + parent_educ:wkly_study_hours 10 1256.7 74094 3157.4
## + ethnic_group:parent_educ 20 2385.2 72965 3168.4
##
## Step: AIC=3144.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:parent_educ +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 803.3 76779 3140.5
## - ethnic_group:test_prep 4 583.4 76559 3140.8
## - parent_marital_status:practice_sport 4 607.7 76583 3140.9
## - test_prep:practice_sport 2 130.4 76106 3141.3
## - practice_sport:is_first_child 2 230.6 76206 3142.0
## - gender:transport_means 1 2.2 75978 3142.3
## - lunch_type:is_first_child 1 2.4 75978 3142.3
## - gender:is_first_child 1 8.7 75984 3142.3
## - gender:test_prep 1 14.5 75990 3142.4
## - test_prep:transport_means 1 15.5 75991 3142.4
## - gender:wkly_study_hours 2 283.2 76259 3142.4
## - lunch_type:test_prep 1 62.2 76038 3142.7
## - transport_means:wkly_study_hours 2 331.5 76307 3142.8
## - test_prep:is_first_child 1 78.2 76054 3142.9
## - gender:lunch_type 1 98.6 76074 3143.0
## - practice_sport:wkly_study_hours 4 895.9 76871 3143.2
## - ethnic_group:lunch_type 4 898.8 76874 3143.2
## - lunch_type:parent_marital_status 2 387.7 76363 3143.2
## - is_first_child:wkly_study_hours 2 485.3 76461 3144.0
## - lunch_type:transport_means 1 230.9 76206 3144.0
## - gender:practice_sport 2 505.5 76481 3144.2
## <none> 75975 3144.2
## - test_prep:parent_marital_status 2 573.9 76549 3144.7
## - lunch_type:wkly_study_hours 2 580.0 76555 3144.7
## - practice_sport:transport_means 2 587.3 76563 3144.8
## - test_prep:wkly_study_hours 2 723.8 76699 3145.8
## - ethnic_group:parent_marital_status 9 2606.7 78582 3146.1
## - ethnic_group:transport_means 4 1335.3 77311 3146.5
## - parent_educ:is_first_child 5 1638.2 77614 3146.8
## + gender:ethnic_group 4 625.0 75350 3147.4
## - parent_educ:practice_sport 10 3044.3 79020 3147.4
## - is_first_child:transport_means 1 745.1 76720 3148.0
## + parent_educ:transport_means 5 748.8 75227 3148.4
## - ethnic_group:is_first_child 4 1618.4 77594 3148.7
## - parent_educ:parent_marital_status 13 4147.5 80123 3149.6
## + gender:parent_marital_status 3 53.1 75922 3149.8
## - parent_marital_status:wkly_study_hours 4 1869.3 77845 3150.6
## - lunch_type:practice_sport 2 1362.2 77338 3150.7
## - parent_marital_status:transport_means 3 1625.8 77601 3150.7
## + parent_educ:test_prep 5 378.4 75597 3151.3
## + parent_educ:lunch_type 5 249.3 75726 3152.3
## + ethnic_group:practice_sport 8 990.4 74985 3152.5
## + ethnic_group:wkly_study_hours 8 951.0 75024 3152.8
## + parent_educ:wkly_study_hours 10 1276.1 74699 3154.3
## - parent_marital_status:is_first_child 2 1937.3 77913 3155.1
## + ethnic_group:parent_educ 20 2426.2 73549 3165.1
##
## Step: AIC=3140.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 579.8 77359 3136.9
## - parent_marital_status:practice_sport 4 610.1 77389 3137.1
## - test_prep:practice_sport 2 174.1 76953 3137.8
## - gender:transport_means 1 2.3 76781 3138.5
## - lunch_type:is_first_child 1 3.9 76783 3138.5
## - gender:is_first_child 1 8.2 76787 3138.5
## - ethnic_group:lunch_type 4 793.2 77572 3138.5
## - test_prep:transport_means 1 8.6 76787 3138.5
## - practice_sport:is_first_child 2 271.5 77050 3138.5
## - gender:test_prep 1 13.6 76792 3138.6
## - gender:wkly_study_hours 2 305.8 77084 3138.8
## - transport_means:wkly_study_hours 2 333.7 77112 3139.0
## - practice_sport:wkly_study_hours 4 866.5 77645 3139.1
## - lunch_type:test_prep 1 89.9 76869 3139.1
## - lunch_type:parent_marital_status 2 356.6 77135 3139.2
## - gender:lunch_type 1 106.1 76885 3139.3
## - test_prep:is_first_child 1 121.6 76900 3139.4
## - gender:practice_sport 2 513.8 77292 3140.4
## <none> 76779 3140.4
## - test_prep:parent_marital_status 2 543.9 77323 3140.6
## - is_first_child:wkly_study_hours 2 547.5 77326 3140.6
## - practice_sport:transport_means 2 576.1 77355 3140.9
## - lunch_type:transport_means 1 337.5 77116 3141.0
## - lunch_type:wkly_study_hours 2 602.4 77381 3141.1
## - ethnic_group:parent_marital_status 9 2495.1 79274 3141.3
## - parent_educ:is_first_child 5 1473.0 78252 3141.7
## - test_prep:wkly_study_hours 2 793.8 77573 3142.5
## - parent_educ:practice_sport 10 2997.2 79776 3143.0
## - ethnic_group:transport_means 4 1487.1 78266 3143.8
## - is_first_child:transport_means 1 729.0 77508 3144.0
## + gender:parent_educ 5 803.3 75975 3144.2
## - ethnic_group:is_first_child 4 1574.1 78353 3144.4
## + parent_educ:transport_means 5 771.5 76007 3144.5
## + gender:ethnic_group 4 463.6 76315 3144.9
## + gender:parent_marital_status 3 49.7 76729 3146.1
## - lunch_type:practice_sport 2 1378.5 78157 3146.9
## - parent_marital_status:wkly_study_hours 4 1932.2 78711 3147.1
## - parent_marital_status:transport_means 3 1712.3 78491 3147.5
## + parent_educ:test_prep 5 325.1 76454 3147.9
## + parent_educ:lunch_type 5 253.8 76525 3148.5
## - parent_educ:parent_marital_status 13 4591.9 81371 3148.7
## + ethnic_group:practice_sport 8 953.6 75825 3149.1
## + ethnic_group:wkly_study_hours 8 934.0 75845 3149.2
## + parent_educ:wkly_study_hours 10 1262.9 75516 3150.7
## - parent_marital_status:is_first_child 2 1915.9 78695 3151.0
## + ethnic_group:parent_educ 20 2444.2 74335 3161.4
##
## Step: AIC=3136.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 533.2 77892 3132.9
## - test_prep:practice_sport 2 161.1 77520 3134.1
## - ethnic_group:lunch_type 4 747.4 78106 3134.6
## - gender:transport_means 1 1.4 77360 3134.9
## - gender:is_first_child 1 3.8 77362 3134.9
## - lunch_type:is_first_child 1 8.7 77367 3135.0
## - gender:test_prep 1 10.2 77369 3135.0
## - test_prep:transport_means 1 11.0 77370 3135.0
## - gender:wkly_study_hours 2 274.9 77633 3135.0
## - practice_sport:is_first_child 2 307.1 77666 3135.2
## - practice_sport:wkly_study_hours 4 846.0 78204 3135.3
## - transport_means:wkly_study_hours 2 321.1 77680 3135.3
## - lunch_type:test_prep 1 90.8 77449 3135.6
## - lunch_type:parent_marital_status 2 359.1 77718 3135.6
## - gender:lunch_type 1 96.6 77455 3135.6
## - test_prep:is_first_child 1 102.3 77461 3135.7
## - test_prep:parent_marital_status 2 465.8 77824 3136.4
## - gender:practice_sport 2 500.6 77859 3136.7
## - is_first_child:wkly_study_hours 2 507.8 77866 3136.8
## <none> 77359 3136.9
## - ethnic_group:parent_marital_status 9 2421.8 79780 3137.1
## - practice_sport:transport_means 2 583.7 77942 3137.3
## - lunch_type:transport_means 1 352.8 77711 3137.6
## - lunch_type:wkly_study_hours 2 639.5 77998 3137.8
## - parent_educ:is_first_child 5 1498.7 78857 3138.2
## - parent_educ:practice_sport 10 3002.3 80361 3139.3
## - test_prep:wkly_study_hours 2 860.1 78219 3139.4
## - is_first_child:transport_means 1 727.5 78086 3140.4
## + ethnic_group:test_prep 4 579.8 76779 3140.4
## + parent_educ:transport_means 5 819.8 76539 3140.6
## + gender:parent_educ 5 799.7 76559 3140.8
## - ethnic_group:is_first_child 4 1599.6 78958 3141.0
## - ethnic_group:transport_means 4 1611.9 78970 3141.1
## + gender:ethnic_group 4 374.8 76984 3142.0
## + gender:parent_marital_status 3 72.6 77286 3142.3
## - parent_marital_status:wkly_study_hours 4 1929.3 79288 3143.4
## - lunch_type:practice_sport 2 1417.0 78776 3143.6
## - parent_marital_status:transport_means 3 1711.0 79070 3143.8
## + parent_educ:test_prep 5 315.5 77043 3144.5
## + parent_educ:lunch_type 5 243.5 77115 3145.0
## - parent_educ:parent_marital_status 13 4692.5 82051 3145.6
## + ethnic_group:practice_sport 8 942.1 76416 3145.7
## + ethnic_group:wkly_study_hours 8 878.6 76480 3146.2
## + parent_educ:wkly_study_hours 10 1190.6 76168 3147.7
## - parent_marital_status:is_first_child 2 2031.7 79390 3148.2
## + ethnic_group:parent_educ 20 2464.6 74894 3157.8
##
## Step: AIC=3132.94
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 368.2 78260 3129.7
## - test_prep:practice_sport 2 150.3 78042 3130.1
## - ethnic_group:lunch_type 4 775.5 78667 3130.8
## - practice_sport:is_first_child 2 265.2 78157 3130.9
## - gender:is_first_child 1 1.6 77893 3130.9
## - gender:transport_means 1 3.6 77895 3131.0
## - test_prep:transport_means 1 9.1 77901 3131.0
## - lunch_type:is_first_child 1 14.4 77906 3131.1
## - gender:test_prep 1 22.0 77914 3131.1
## - gender:wkly_study_hours 2 316.5 78208 3131.3
## - transport_means:wkly_study_hours 2 323.4 78215 3131.4
## - ethnic_group:parent_marital_status 10 2477.6 80369 3131.4
## - practice_sport:wkly_study_hours 4 878.9 78771 3131.6
## - test_prep:is_first_child 1 96.0 77988 3131.7
## - lunch_type:test_prep 1 100.7 77992 3131.7
## - gender:lunch_type 1 110.2 78002 3131.8
## - test_prep:parent_marital_status 2 413.7 78305 3132.1
## - is_first_child:wkly_study_hours 2 514.9 78407 3132.8
## - gender:practice_sport 2 523.4 78415 3132.9
## <none> 77892 3132.9
## - practice_sport:transport_means 2 544.8 78437 3133.1
## - lunch_type:transport_means 1 315.9 78208 3133.3
## - lunch_type:wkly_study_hours 2 646.8 78539 3133.8
## - parent_educ:is_first_child 5 1450.7 79342 3133.8
## - parent_educ:practice_sport 10 2867.2 80759 3134.3
## - ethnic_group:transport_means 4 1416.9 79309 3135.6
## - test_prep:wkly_study_hours 2 963.4 78855 3136.2
## - is_first_child:transport_means 1 722.5 78614 3136.4
## + parent_marital_status:practice_sport 4 533.2 77359 3136.9
## + gender:parent_educ 5 794.5 77097 3136.9
## - ethnic_group:is_first_child 4 1601.7 79493 3136.9
## + parent_educ:transport_means 5 772.0 77120 3137.1
## + ethnic_group:test_prep 4 502.9 77389 3137.1
## - parent_marital_status:wkly_study_hours 5 1966.9 79859 3137.7
## + gender:ethnic_group 4 347.9 77544 3138.3
## + gender:parent_marital_status 3 64.2 77828 3138.5
## - parent_marital_status:transport_means 3 1696.1 79588 3139.7
## - lunch_type:practice_sport 2 1453.7 79345 3139.8
## + parent_educ:test_prep 5 317.5 77574 3140.5
## + ethnic_group:practice_sport 8 1088.4 76803 3140.6
## + parent_educ:lunch_type 5 251.8 77640 3141.0
## + ethnic_group:wkly_study_hours 8 797.6 77094 3142.9
## - parent_educ:parent_marital_status 14 5190.5 83082 3143.0
## + parent_educ:wkly_study_hours 10 1174.0 76718 3144.0
## - parent_marital_status:is_first_child 2 2196.3 80088 3145.3
## + ethnic_group:parent_educ 20 2483.8 75408 3153.8
##
## Step: AIC=3129.72
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 165.1 78425 3127.0
## - practice_sport:is_first_child 2 212.2 78472 3127.3
## - ethnic_group:lunch_type 4 777.4 79037 3127.6
## - gender:is_first_child 1 4.9 78265 3127.8
## - gender:wkly_study_hours 2 271.6 78532 3127.8
## - gender:transport_means 1 6.8 78267 3127.8
## - test_prep:transport_means 1 10.2 78270 3127.8
## - ethnic_group:parent_marital_status 10 2435.5 80696 3127.8
## - lunch_type:is_first_child 1 18.4 78278 3127.9
## - practice_sport:wkly_study_hours 4 826.1 79086 3127.9
## - gender:test_prep 1 38.7 78299 3128.0
## - lunch_type:test_prep 1 84.5 78345 3128.4
## - test_prep:is_first_child 1 94.7 78355 3128.4
## - transport_means:wkly_study_hours 2 361.1 78621 3128.4
## - test_prep:parent_marital_status 2 404.9 78665 3128.8
## - gender:lunch_type 1 155.7 78416 3128.9
## - gender:practice_sport 2 481.8 78742 3129.3
## - is_first_child:wkly_study_hours 2 484.9 78745 3129.4
## <none> 78260 3129.7
## - practice_sport:transport_means 2 535.6 78796 3129.8
## - lunch_type:transport_means 1 321.4 78581 3130.1
## - parent_educ:is_first_child 5 1397.5 79657 3130.2
## - lunch_type:wkly_study_hours 2 592.2 78852 3130.2
## - parent_educ:practice_sport 10 2842.9 81103 3130.8
## - ethnic_group:transport_means 4 1371.7 79632 3132.0
## - test_prep:wkly_study_hours 2 944.1 79204 3132.8
## + lunch_type:parent_marital_status 3 368.2 77892 3132.9
## - is_first_child:transport_means 1 745.6 79006 3133.3
## + parent_educ:transport_means 5 837.1 77423 3133.4
## - ethnic_group:is_first_child 4 1603.9 79864 3133.7
## + ethnic_group:test_prep 4 514.1 77746 3133.8
## + gender:parent_educ 5 758.5 77501 3134.0
## - parent_marital_status:wkly_study_hours 5 1918.3 80178 3134.0
## + gender:parent_marital_status 3 93.8 78166 3135.0
## + gender:ethnic_group 4 302.8 77957 3135.4
## + parent_marital_status:practice_sport 5 542.4 77718 3135.6
## - lunch_type:practice_sport 2 1379.3 79639 3136.0
## - parent_marital_status:transport_means 3 1664.3 79924 3136.1
## + parent_educ:test_prep 5 319.0 77941 3137.3
## + ethnic_group:practice_sport 8 1103.5 77156 3137.3
## + parent_educ:lunch_type 5 272.2 77988 3137.7
## + ethnic_group:wkly_study_hours 8 800.2 77460 3139.7
## + parent_educ:wkly_study_hours 10 1154.0 77106 3141.0
## - parent_marital_status:is_first_child 2 2180.7 80441 3141.9
## - parent_educ:parent_marital_status 14 5685.1 83945 3143.1
## + ethnic_group:parent_educ 20 2274.4 75986 3152.3
##
## Step: AIC=3126.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 10 2362.3 80787 3124.5
## - practice_sport:is_first_child 2 234.6 78660 3124.7
## - gender:wkly_study_hours 2 257.8 78683 3124.9
## - gender:is_first_child 1 2.9 78428 3125.0
## - gender:transport_means 1 6.5 78432 3125.0
## - test_prep:transport_means 1 14.0 78439 3125.1
## - lunch_type:is_first_child 1 17.1 78442 3125.1
## - ethnic_group:lunch_type 4 837.1 79262 3125.2
## - gender:test_prep 1 37.2 78462 3125.2
## - practice_sport:wkly_study_hours 4 865.2 79290 3125.4
## - lunch_type:test_prep 1 92.0 78517 3125.7
## - test_prep:is_first_child 1 99.3 78524 3125.7
## - transport_means:wkly_study_hours 2 387.2 78812 3125.9
## - gender:lunch_type 1 168.8 78594 3126.2
## - test_prep:parent_marital_status 2 444.0 78869 3126.3
## - is_first_child:wkly_study_hours 2 453.2 78878 3126.4
## - practice_sport:transport_means 2 506.4 78931 3126.8
## - gender:practice_sport 2 509.9 78935 3126.8
## <none> 78425 3127.0
## - lunch_type:transport_means 1 319.5 78745 3127.4
## - lunch_type:wkly_study_hours 2 643.8 79069 3127.8
## - parent_educ:practice_sport 10 2891.2 81316 3128.3
## - parent_educ:is_first_child 5 1540.6 79966 3128.4
## - ethnic_group:transport_means 4 1350.2 79775 3129.0
## + test_prep:practice_sport 2 165.1 78260 3129.7
## + lunch_type:parent_marital_status 3 383.1 78042 3130.1
## - test_prep:wkly_study_hours 2 952.3 79377 3130.1
## + parent_educ:transport_means 5 852.2 77573 3130.5
## - is_first_child:transport_means 1 755.8 79181 3130.6
## + gender:parent_educ 5 805.0 77620 3130.9
## - parent_marital_status:wkly_study_hours 5 1874.3 80299 3130.9
## - ethnic_group:is_first_child 4 1614.4 80040 3131.0
## + ethnic_group:test_prep 4 497.3 77928 3131.2
## + gender:parent_marital_status 3 119.3 78306 3132.1
## + gender:ethnic_group 4 285.5 78140 3132.8
## + parent_marital_status:practice_sport 5 529.7 77895 3133.0
## - parent_marital_status:transport_means 3 1654.2 80079 3133.3
## - lunch_type:practice_sport 2 1438.7 79864 3133.7
## + parent_educ:test_prep 5 295.7 78129 3134.7
## + ethnic_group:practice_sport 8 1085.0 77340 3134.8
## + parent_educ:lunch_type 5 267.4 78158 3134.9
## + ethnic_group:wkly_study_hours 8 780.9 77644 3137.1
## + parent_educ:wkly_study_hours 10 1191.5 77234 3137.9
## - parent_marital_status:is_first_child 2 2135.4 80561 3138.8
## - parent_educ:parent_marital_status 14 5615.3 84040 3139.8
## + ethnic_group:parent_educ 20 2354.4 76071 3149.0
##
## Step: AIC=3124.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 134.9 80922 3121.5
## - practice_sport:wkly_study_hours 4 706.5 81494 3121.6
## - gender:wkly_study_hours 2 192.1 80980 3121.9
## - transport_means:wkly_study_hours 2 268.3 81056 3122.4
## - practice_sport:transport_means 2 270.0 81057 3122.4
## - test_prep:parent_marital_status 3 558.2 81346 3122.5
## - test_prep:transport_means 1 12.1 80800 3122.6
## - gender:is_first_child 1 21.6 80809 3122.6
## - gender:transport_means 1 26.2 80814 3122.7
## - lunch_type:is_first_child 1 35.8 80823 3122.7
## - ethnic_group:lunch_type 4 873.8 81661 3122.8
## - parent_educ:practice_sport 10 2583.4 83371 3123.1
## - lunch_type:test_prep 1 87.2 80875 3123.1
## - gender:test_prep 1 91.6 80879 3123.2
## - test_prep:is_first_child 1 138.6 80926 3123.5
## - is_first_child:wkly_study_hours 2 434.4 81222 3123.6
## - gender:lunch_type 1 177.5 80965 3123.8
## - gender:practice_sport 2 524.9 81312 3124.3
## <none> 80787 3124.5
## - lunch_type:wkly_study_hours 2 609.6 81397 3124.9
## - parent_marital_status:wkly_study_hours 6 1735.4 82523 3125.0
## - lunch_type:transport_means 1 384.1 81172 3125.3
## - ethnic_group:is_first_child 4 1283.6 82071 3125.8
## - ethnic_group:transport_means 4 1329.1 82117 3126.1
## - parent_educ:is_first_child 5 1623.5 82411 3126.2
## + ethnic_group:parent_marital_status 10 2362.3 78425 3127.0
## + gender:parent_marital_status 3 436.1 80351 3127.3
## - parent_marital_status:transport_means 3 1233.0 82020 3127.4
## + parent_educ:transport_means 5 917.7 79870 3127.7
## + test_prep:practice_sport 2 91.9 80696 3127.8
## + lunch_type:parent_marital_status 3 338.3 80449 3128.0
## - test_prep:wkly_study_hours 2 1155.0 81942 3128.8
## + ethnic_group:test_prep 4 446.8 80341 3129.2
## + gender:parent_educ 5 707.0 80080 3129.3
## - is_first_child:transport_means 1 981.3 81769 3129.6
## + gender:ethnic_group 4 243.7 80544 3130.7
## + parent_marital_status:practice_sport 6 627.4 80160 3131.9
## - lunch_type:practice_sport 2 1582.8 82370 3131.9
## + parent_educ:test_prep 5 304.0 80483 3132.2
## + parent_educ:lunch_type 5 266.7 80521 3132.5
## + ethnic_group:practice_sport 8 1071.0 79716 3132.6
## - parent_marital_status:is_first_child 3 2014.8 82802 3133.0
## - parent_educ:parent_marital_status 15 5583.0 86370 3133.9
## + parent_educ:wkly_study_hours 10 1312.1 79475 3134.8
## + ethnic_group:wkly_study_hours 8 702.7 80085 3135.3
## + ethnic_group:parent_educ 20 2394.3 78393 3146.7
##
## Step: AIC=3121.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 746.1 81668 3118.9
## - gender:wkly_study_hours 2 197.4 81120 3118.9
## - practice_sport:transport_means 2 256.1 81178 3119.3
## - test_prep:parent_marital_status 3 542.8 81465 3119.4
## - transport_means:wkly_study_hours 2 274.7 81197 3119.5
## - test_prep:transport_means 1 12.3 80935 3119.6
## - gender:is_first_child 1 25.8 80948 3119.7
## - lunch_type:is_first_child 1 27.4 80950 3119.7
## - gender:transport_means 1 32.3 80955 3119.7
## - parent_educ:practice_sport 10 2575.3 83498 3119.9
## - ethnic_group:lunch_type 4 901.1 81823 3120.0
## - lunch_type:test_prep 1 98.2 81021 3120.2
## - gender:test_prep 1 100.2 81023 3120.2
## - test_prep:is_first_child 1 105.9 81028 3120.2
## - is_first_child:wkly_study_hours 2 409.4 81332 3120.4
## - gender:lunch_type 1 186.1 81108 3120.8
## - gender:practice_sport 2 520.7 81443 3121.2
## <none> 80922 3121.5
## - lunch_type:wkly_study_hours 2 614.4 81537 3121.9
## - parent_marital_status:wkly_study_hours 6 1743.9 82666 3122.0
## - lunch_type:transport_means 1 376.8 81299 3122.2
## - ethnic_group:transport_means 4 1280.0 82202 3122.7
## - parent_educ:is_first_child 5 1598.0 82520 3123.0
## - ethnic_group:is_first_child 4 1368.9 82291 3123.4
## - parent_marital_status:transport_means 3 1178.7 82101 3124.0
## + gender:parent_marital_status 3 414.4 80508 3124.4
## + practice_sport:is_first_child 2 134.9 80787 3124.5
## + test_prep:practice_sport 2 104.1 80818 3124.7
## + ethnic_group:parent_marital_status 10 2262.6 78660 3124.7
## + parent_educ:transport_means 5 873.3 80049 3125.1
## + lunch_type:parent_marital_status 3 286.4 80636 3125.4
## - test_prep:wkly_study_hours 2 1121.2 82044 3125.6
## + ethnic_group:test_prep 4 475.9 80446 3126.0
## + gender:parent_educ 5 724.6 80198 3126.2
## - is_first_child:transport_means 1 1054.5 81977 3127.1
## + gender:ethnic_group 4 280.3 80642 3127.4
## - lunch_type:practice_sport 2 1568.5 82491 3128.8
## + parent_educ:test_prep 5 352.1 80570 3128.9
## + parent_educ:lunch_type 5 272.5 80650 3129.5
## + parent_marital_status:practice_sport 6 543.3 80379 3129.5
## - parent_marital_status:is_first_child 3 1952.1 82874 3129.5
## + ethnic_group:practice_sport 8 1035.2 79887 3129.9
## - parent_educ:parent_marital_status 15 5525.4 86448 3130.4
## + parent_educ:wkly_study_hours 10 1304.2 79618 3131.9
## + ethnic_group:wkly_study_hours 8 727.5 80195 3132.1
## + ethnic_group:parent_educ 20 2361.2 78561 3144.0
##
## Step: AIC=3118.88
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 179.7 81848 3116.2
## - practice_sport:transport_means 2 229.3 81898 3116.5
## - ethnic_group:lunch_type 4 793.3 82462 3116.6
## - test_prep:parent_marital_status 3 560.0 82228 3116.9
## - test_prep:transport_means 1 11.3 81680 3117.0
## - gender:transport_means 1 15.7 81684 3117.0
## - transport_means:wkly_study_hours 2 295.9 81964 3117.0
## - parent_educ:practice_sport 10 2564.2 84233 3117.1
## - gender:is_first_child 1 44.9 81713 3117.2
## - lunch_type:is_first_child 1 69.4 81738 3117.4
## - gender:test_prep 1 88.2 81757 3117.5
## - lunch_type:test_prep 1 131.6 81800 3117.8
## - test_prep:is_first_child 1 135.8 81804 3117.9
## - gender:lunch_type 1 202.3 81871 3118.3
## - is_first_child:wkly_study_hours 2 498.4 82167 3118.5
## <none> 81668 3118.9
## - lunch_type:wkly_study_hours 2 556.9 82225 3118.9
## - gender:practice_sport 2 560.6 82229 3118.9
## - lunch_type:transport_means 1 336.4 82005 3119.3
## - parent_educ:is_first_child 5 1501.0 83169 3119.6
## - parent_marital_status:wkly_study_hours 6 1807.4 83476 3119.8
## - ethnic_group:transport_means 4 1251.4 82920 3119.8
## - ethnic_group:is_first_child 4 1415.5 83084 3121.0
## + practice_sport:wkly_study_hours 4 746.1 80922 3121.5
## + practice_sport:is_first_child 2 174.5 81494 3121.6
## - parent_marital_status:transport_means 3 1236.0 82904 3121.7
## + test_prep:practice_sport 2 136.1 81532 3121.9
## + gender:parent_marital_status 3 401.9 81267 3122.0
## + parent_educ:transport_means 5 945.4 80723 3122.0
## + lunch_type:parent_marital_status 3 219.3 81449 3123.3
## - test_prep:wkly_study_hours 2 1185.6 82854 3123.4
## + ethnic_group:test_prep 4 471.0 81197 3123.5
## + ethnic_group:parent_marital_status 10 2103.1 79565 3123.5
## + gender:parent_educ 5 705.1 80963 3123.8
## + gender:ethnic_group 4 333.0 81335 3124.5
## - is_first_child:transport_means 1 1069.1 82737 3124.6
## - lunch_type:practice_sport 2 1506.1 83174 3125.7
## + parent_educ:test_prep 5 375.4 81293 3126.2
## + parent_educ:lunch_type 5 326.2 81342 3126.5
## - parent_educ:parent_marital_status 15 5411.4 87080 3126.7
## - parent_marital_status:is_first_child 3 1942.8 83611 3126.8
## + parent_marital_status:practice_sport 6 469.0 81199 3127.5
## + ethnic_group:practice_sport 8 969.6 80699 3127.8
## + ethnic_group:wkly_study_hours 8 807.6 80861 3129.0
## + parent_educ:wkly_study_hours 10 1140.4 80528 3130.6
## + ethnic_group:parent_educ 20 2482.9 79186 3140.7
##
## Step: AIC=3116.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:lunch_type + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 791.6 82640 3113.8
## - practice_sport:transport_means 2 245.4 82094 3113.9
## - test_prep:parent_marital_status 3 545.1 82393 3114.1
## - test_prep:transport_means 1 11.0 81859 3114.2
## - transport_means:wkly_study_hours 2 290.0 82138 3114.3
## - gender:transport_means 1 18.5 81867 3114.3
## - parent_educ:practice_sport 10 2558.1 84406 3114.3
## - gender:is_first_child 1 48.8 81897 3114.5
## - lunch_type:is_first_child 1 68.8 81917 3114.7
## - gender:test_prep 1 110.7 81959 3115.0
## - lunch_type:test_prep 1 122.5 81971 3115.1
## - test_prep:is_first_child 1 162.3 82010 3115.3
## - gender:lunch_type 1 171.5 82020 3115.4
## - is_first_child:wkly_study_hours 2 495.3 82343 3115.7
## - lunch_type:wkly_study_hours 2 509.0 82357 3115.8
## <none> 81848 3116.2
## - gender:practice_sport 2 570.2 82418 3116.3
## - lunch_type:transport_means 1 328.3 82176 3116.5
## - parent_educ:is_first_child 5 1504.7 83353 3116.9
## - ethnic_group:transport_means 4 1252.8 83101 3117.1
## - ethnic_group:is_first_child 4 1338.1 83186 3117.7
## - parent_marital_status:wkly_study_hours 6 2060.0 83908 3118.8
## + practice_sport:is_first_child 2 182.7 81665 3118.9
## + gender:wkly_study_hours 2 179.7 81668 3118.9
## - parent_marital_status:transport_means 3 1218.2 83066 3118.9
## + practice_sport:wkly_study_hours 4 728.4 81120 3118.9
## + test_prep:practice_sport 2 138.9 81709 3119.2
## + gender:parent_marital_status 3 407.2 81441 3119.2
## + parent_educ:transport_means 5 888.5 80960 3119.7
## - test_prep:wkly_study_hours 2 1175.5 83024 3120.6
## + lunch_type:parent_marital_status 3 191.5 81657 3120.8
## + gender:parent_educ 5 730.7 81117 3120.9
## + ethnic_group:test_prep 4 436.0 81412 3121.0
## + ethnic_group:parent_marital_status 10 2063.5 79785 3121.1
## - is_first_child:transport_means 1 1003.7 82852 3121.4
## + gender:ethnic_group 4 373.8 81474 3121.5
## - lunch_type:practice_sport 2 1498.1 83346 3122.9
## - parent_marital_status:is_first_child 3 1869.2 83717 3123.5
## + parent_educ:test_prep 5 367.9 81480 3123.5
## - parent_educ:parent_marital_status 15 5370.9 87219 3123.7
## + parent_educ:lunch_type 5 307.2 81541 3124.0
## + parent_marital_status:practice_sport 6 474.3 81374 3124.8
## + ethnic_group:practice_sport 8 1015.8 80832 3124.8
## + ethnic_group:wkly_study_hours 8 786.1 81062 3126.5
## + parent_educ:wkly_study_hours 10 1222.9 80625 3127.3
## + ethnic_group:parent_educ 20 2486.4 79362 3138.0
##
## Step: AIC=3113.85
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 207.3 82847 3111.3
## - parent_educ:practice_sport 10 2516.6 85156 3111.6
## - test_prep:transport_means 1 10.1 82650 3111.9
## - gender:transport_means 1 13.8 82653 3111.9
## - gender:is_first_child 1 41.3 82681 3112.2
## - transport_means:wkly_study_hours 2 339.2 82979 3112.3
## - test_prep:parent_marital_status 3 629.1 83269 3112.3
## - lunch_type:is_first_child 1 80.4 82720 3112.4
## - gender:test_prep 1 135.3 82775 3112.8
## - test_prep:is_first_child 1 142.8 82782 3112.9
## - lunch_type:test_prep 1 144.5 82784 3112.9
## - lunch_type:wkly_study_hours 2 428.9 83069 3112.9
## - gender:lunch_type 1 191.2 82831 3113.2
## - gender:practice_sport 2 488.0 83128 3113.3
## - is_first_child:wkly_study_hours 2 498.0 83138 3113.4
## <none> 82640 3113.8
## - ethnic_group:is_first_child 4 1132.4 83772 3113.9
## - ethnic_group:transport_means 4 1167.1 83807 3114.1
## - parent_educ:is_first_child 5 1534.0 84174 3114.7
## - lunch_type:transport_means 1 438.1 83078 3115.0
## - parent_marital_status:transport_means 3 1154.2 83794 3116.0
## + ethnic_group:lunch_type 4 791.6 81848 3116.2
## + practice_sport:is_first_child 2 203.4 82436 3116.4
## + test_prep:practice_sport 2 188.0 82452 3116.5
## + gender:wkly_study_hours 2 178.0 82462 3116.6
## - parent_marital_status:wkly_study_hours 6 2096.2 84736 3116.6
## + parent_educ:transport_means 5 990.3 81649 3116.7
## + gender:parent_marital_status 3 400.6 82239 3117.0
## + practice_sport:wkly_study_hours 4 624.4 82015 3117.4
## + ethnic_group:parent_marital_status 10 2132.2 80507 3118.4
## + lunch_type:parent_marital_status 3 186.2 82454 3118.5
## - test_prep:wkly_study_hours 2 1230.2 83870 3118.6
## - is_first_child:transport_means 1 991.0 83631 3118.9
## + ethnic_group:test_prep 4 387.6 82252 3119.1
## + gender:ethnic_group 4 380.7 82259 3119.1
## + gender:parent_educ 5 625.8 82014 3119.4
## - parent_educ:parent_marital_status 15 5161.0 87801 3119.6
## - parent_marital_status:is_first_child 3 1814.6 84454 3120.7
## + parent_educ:test_prep 5 407.8 82232 3120.9
## - lunch_type:practice_sport 2 1597.2 84237 3121.2
## + parent_educ:lunch_type 5 333.4 82306 3121.5
## + ethnic_group:practice_sport 8 1057.8 81582 3122.2
## + parent_marital_status:practice_sport 6 482.2 82158 3122.4
## + ethnic_group:wkly_study_hours 8 816.7 81823 3124.0
## + parent_educ:wkly_study_hours 10 1061.0 81579 3126.2
## + ethnic_group:parent_educ 20 2629.1 80011 3134.8
##
## Step: AIC=3111.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 2466.4 85313 3108.6
## - test_prep:transport_means 1 7.1 82854 3109.4
## - gender:transport_means 1 13.8 82861 3109.4
## - gender:is_first_child 1 56.2 82903 3109.7
## - lunch_type:is_first_child 1 71.3 82918 3109.8
## - transport_means:wkly_study_hours 2 357.8 83205 3109.9
## - test_prep:parent_marital_status 3 644.8 83492 3109.9
## - gender:test_prep 1 131.9 82979 3110.3
## - lunch_type:wkly_study_hours 2 420.4 83267 3110.3
## - test_prep:is_first_child 1 147.4 82994 3110.4
## - lunch_type:test_prep 1 170.0 83017 3110.5
## - gender:practice_sport 2 458.5 83305 3110.6
## - gender:lunch_type 1 191.5 83039 3110.7
## - is_first_child:wkly_study_hours 2 491.5 83338 3110.8
## - ethnic_group:is_first_child 4 1114.2 83961 3111.2
## <none> 82847 3111.3
## - ethnic_group:transport_means 4 1218.0 84065 3111.9
## - parent_educ:is_first_child 5 1544.3 84391 3112.2
## - lunch_type:transport_means 1 450.3 83297 3112.5
## - parent_marital_status:transport_means 3 1149.8 83997 3113.5
## + practice_sport:transport_means 2 207.3 82640 3113.8
## + ethnic_group:lunch_type 4 753.5 82094 3113.9
## + gender:wkly_study_hours 2 193.1 82654 3113.9
## + practice_sport:is_first_child 2 183.8 82663 3114.0
## + test_prep:practice_sport 2 173.2 82674 3114.1
## - parent_marital_status:wkly_study_hours 6 2116.7 84964 3114.2
## + gender:parent_marital_status 3 364.2 82483 3114.7
## + practice_sport:wkly_study_hours 4 605.0 82242 3115.0
## + parent_educ:transport_means 5 874.3 81973 3115.1
## + lunch_type:parent_marital_status 3 180.4 82667 3116.0
## - test_prep:wkly_study_hours 2 1235.2 84082 3116.1
## + ethnic_group:test_prep 4 396.0 82451 3116.5
## + gender:ethnic_group 4 377.0 82470 3116.6
## - parent_educ:parent_marital_status 15 5138.6 87986 3116.8
## - is_first_child:transport_means 1 1062.2 83909 3116.8
## + gender:parent_educ 5 597.8 82249 3117.1
## + ethnic_group:parent_marital_status 10 1954.3 80893 3117.2
## - parent_marital_status:is_first_child 3 1809.3 84656 3118.1
## + parent_educ:test_prep 5 434.0 82413 3118.2
## - lunch_type:practice_sport 2 1585.6 84433 3118.5
## + parent_educ:lunch_type 5 376.4 82471 3118.6
## + ethnic_group:practice_sport 8 1073.6 81773 3119.6
## + parent_marital_status:practice_sport 6 447.4 82400 3120.1
## + ethnic_group:wkly_study_hours 8 821.6 82025 3121.4
## + parent_educ:wkly_study_hours 10 1023.1 81824 3124.0
## + ethnic_group:parent_educ 20 2651.9 80195 3132.1
##
## Step: AIC=3108.64
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 3 528.2 85842 3106.3
## - transport_means:wkly_study_hours 2 252.8 85566 3106.4
## - test_prep:transport_means 1 6.1 85320 3106.7
## - gender:transport_means 1 53.5 85367 3107.0
## - gender:is_first_child 1 69.0 85382 3107.1
## - gender:practice_sport 2 371.9 85685 3107.2
## - lunch_type:is_first_child 1 89.0 85402 3107.2
## - gender:lunch_type 1 128.6 85442 3107.5
## - lunch_type:test_prep 1 168.7 85482 3107.8
## - gender:test_prep 1 169.6 85483 3107.8
## - test_prep:is_first_child 1 189.4 85503 3107.9
## - is_first_child:wkly_study_hours 2 501.2 85815 3108.1
## - lunch_type:wkly_study_hours 2 501.8 85815 3108.1
## <none> 85313 3108.6
## - ethnic_group:is_first_child 4 1176.4 86490 3108.7
## - lunch_type:transport_means 1 350.4 85664 3109.1
## - ethnic_group:transport_means 4 1384.3 86698 3110.1
## - test_prep:wkly_study_hours 2 930.9 86244 3111.0
## + parent_educ:practice_sport 10 2466.4 82847 3111.3
## + gender:wkly_study_hours 2 187.2 85126 3111.3
## - parent_educ:is_first_child 5 1861.6 87175 3111.4
## + practice_sport:is_first_child 2 173.2 85140 3111.4
## + test_prep:practice_sport 2 172.7 85141 3111.4
## + practice_sport:transport_means 2 157.1 85156 3111.6
## + ethnic_group:lunch_type 4 725.6 84588 3111.6
## - parent_marital_status:wkly_study_hours 6 2229.8 87543 3111.9
## - parent_marital_status:transport_means 3 1345.0 86658 3111.9
## + gender:parent_marital_status 3 380.5 84933 3112.0
## - is_first_child:transport_means 1 813.3 86127 3112.2
## + practice_sport:wkly_study_hours 4 575.3 84738 3112.7
## + parent_educ:transport_means 5 848.1 84465 3112.7
## - lunch_type:practice_sport 2 1258.9 86572 3113.3
## + lunch_type:parent_marital_status 3 167.1 85146 3113.5
## + ethnic_group:test_prep 4 430.7 84883 3113.7
## + gender:ethnic_group 4 394.4 84919 3113.9
## + gender:parent_educ 5 656.9 84657 3114.1
## - parent_marital_status:is_first_child 3 1770.1 87084 3114.8
## + parent_educ:lunch_type 5 556.2 84757 3114.8
## + parent_educ:test_prep 5 401.2 84912 3115.9
## + ethnic_group:practice_sport 8 1164.5 84149 3116.5
## - parent_educ:parent_marital_status 15 5674.3 90988 3116.6
## + ethnic_group:parent_marital_status 10 1651.0 83662 3117.1
## + parent_marital_status:practice_sport 6 334.6 84979 3118.3
## + ethnic_group:wkly_study_hours 8 773.4 84540 3119.3
## + parent_educ:wkly_study_hours 10 1137.2 84176 3120.7
## + ethnic_group:parent_educ 20 2585.1 82728 3130.5
##
## Step: AIC=3106.28
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 246.8 86088 3104.0
## - test_prep:transport_means 1 16.2 85858 3104.4
## - gender:transport_means 1 41.8 85883 3104.6
## - lunch_type:is_first_child 1 80.3 85922 3104.8
## - gender:is_first_child 1 80.8 85922 3104.8
## - gender:practice_sport 2 391.2 86233 3105.0
## - gender:lunch_type 1 133.0 85975 3105.2
## - gender:test_prep 1 156.6 85998 3105.4
## - lunch_type:test_prep 1 167.4 86009 3105.4
## - lunch_type:wkly_study_hours 2 517.9 86359 3105.8
## - is_first_child:wkly_study_hours 2 539.2 86381 3106.0
## - test_prep:is_first_child 1 264.1 86106 3106.1
## <none> 85842 3106.3
## - ethnic_group:is_first_child 4 1209.8 87051 3106.5
## - lunch_type:transport_means 1 355.0 86197 3106.7
## - ethnic_group:transport_means 4 1370.0 87212 3107.6
## - parent_educ:is_first_child 5 1803.5 87645 3108.6
## - test_prep:wkly_study_hours 2 922.7 86764 3108.6
## + test_prep:parent_marital_status 3 528.2 85313 3108.6
## + test_prep:practice_sport 2 227.2 85614 3108.7
## + ethnic_group:lunch_type 4 794.7 85047 3108.8
## + gender:wkly_study_hours 2 191.1 85650 3109.0
## + practice_sport:transport_means 2 166.2 85675 3109.1
## + practice_sport:is_first_child 2 165.9 85676 3109.1
## - parent_marital_status:wkly_study_hours 6 2221.9 88063 3109.4
## - is_first_child:transport_means 1 764.1 86606 3109.5
## + parent_educ:practice_sport 10 2349.8 83492 3109.9
## - parent_marital_status:transport_means 3 1470.4 87312 3110.3
## + gender:parent_marital_status 3 286.9 85555 3110.3
## + parent_educ:transport_means 5 862.9 84979 3110.3
## + practice_sport:wkly_study_hours 4 547.4 85294 3110.5
## - lunch_type:practice_sport 2 1236.0 87078 3110.7
## + lunch_type:parent_marital_status 3 214.5 85627 3110.8
## + gender:ethnic_group 4 426.1 85415 3111.3
## + ethnic_group:test_prep 4 419.6 85422 3111.4
## + gender:parent_educ 5 621.8 85220 3112.0
## + parent_educ:lunch_type 5 563.6 85278 3112.4
## - parent_educ:parent_marital_status 15 5469.5 91311 3112.7
## - parent_marital_status:is_first_child 3 1845.3 87687 3112.8
## + parent_educ:test_prep 5 377.3 85464 3113.7
## + ethnic_group:practice_sport 8 1128.8 84713 3114.5
## + parent_marital_status:practice_sport 6 382.9 85459 3115.6
## + ethnic_group:parent_marital_status 11 1760.9 84081 3116.1
## + ethnic_group:wkly_study_hours 8 867.5 84974 3116.3
## + parent_educ:wkly_study_hours 10 1216.0 84626 3117.9
## + ethnic_group:parent_educ 20 2671.7 83170 3127.6
##
## Step: AIC=3103.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 7.5 86096 3102.0
## - gender:transport_means 1 39.1 86127 3102.2
## - gender:is_first_child 1 67.5 86156 3102.4
## - lunch_type:is_first_child 1 74.0 86162 3102.5
## - gender:lunch_type 1 121.2 86210 3102.8
## - gender:practice_sport 2 425.9 86514 3102.9
## - gender:test_prep 1 140.2 86228 3102.9
## - lunch_type:test_prep 1 153.5 86242 3103.0
## - lunch_type:wkly_study_hours 2 549.2 86638 3103.7
## - test_prep:is_first_child 1 279.5 86368 3103.9
## <none> 86088 3104.0
## - is_first_child:wkly_study_hours 2 592.9 86681 3104.0
## - lunch_type:transport_means 1 345.6 86434 3104.3
## - ethnic_group:is_first_child 4 1229.5 87318 3104.3
## - test_prep:wkly_study_hours 2 872.0 86960 3105.9
## - ethnic_group:transport_means 4 1465.2 87554 3105.9
## + test_prep:practice_sport 2 258.1 85830 3106.2
## + ethnic_group:lunch_type 4 835.7 85253 3106.2
## + transport_means:wkly_study_hours 2 246.8 85842 3106.3
## + test_prep:parent_marital_status 3 522.1 85566 3106.4
## - parent_educ:is_first_child 5 1848.6 87937 3106.5
## + practice_sport:transport_means 2 184.0 85904 3106.7
## + practice_sport:is_first_child 2 182.1 85906 3106.7
## + gender:wkly_study_hours 2 180.1 85908 3106.7
## - is_first_child:transport_means 1 769.9 86858 3107.2
## - parent_marital_status:wkly_study_hours 6 2303.2 88392 3107.6
## - parent_marital_status:transport_means 3 1454.0 87542 3107.9
## + practice_sport:wkly_study_hours 4 564.7 85524 3108.1
## + gender:parent_marital_status 3 272.1 85816 3108.1
## + parent_educ:practice_sport 10 2249.6 83839 3108.3
## + parent_educ:transport_means 5 808.8 85280 3108.4
## + lunch_type:parent_marital_status 3 219.1 85869 3108.5
## - lunch_type:practice_sport 2 1254.1 87342 3108.5
## + gender:ethnic_group 4 458.6 85630 3108.8
## + ethnic_group:test_prep 4 414.0 85674 3109.1
## + gender:parent_educ 5 674.2 85414 3109.3
## + parent_educ:lunch_type 5 590.9 85497 3109.9
## - parent_marital_status:is_first_child 3 1791.3 87880 3110.1
## - parent_educ:parent_marital_status 15 5445.9 91534 3110.2
## + parent_educ:test_prep 5 377.4 85711 3111.4
## + ethnic_group:practice_sport 8 1152.6 84936 3112.0
## + parent_marital_status:practice_sport 6 396.9 85691 3113.2
## + ethnic_group:parent_marital_status 11 1695.5 84393 3114.2
## + ethnic_group:wkly_study_hours 8 714.6 85374 3115.1
## + parent_educ:wkly_study_hours 10 1220.0 84868 3115.6
## + ethnic_group:parent_educ 20 2613.0 83475 3125.8
##
## Step: AIC=3102.03
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 42.1 86138 3100.3
## - gender:is_first_child 1 67.9 86164 3100.5
## - lunch_type:is_first_child 1 77.5 86173 3100.6
## - gender:lunch_type 1 124.5 86220 3100.9
## - gender:practice_sport 2 423.6 86519 3100.9
## - gender:test_prep 1 138.2 86234 3101.0
## - lunch_type:test_prep 1 154.4 86250 3101.1
## - lunch_type:wkly_study_hours 2 541.9 86638 3101.7
## - test_prep:is_first_child 1 280.9 86377 3101.9
## <none> 86096 3102.0
## - is_first_child:wkly_study_hours 2 601.9 86698 3102.1
## - ethnic_group:is_first_child 4 1222.9 87319 3102.3
## - lunch_type:transport_means 1 341.8 86438 3102.4
## - test_prep:wkly_study_hours 2 866.7 86963 3103.9
## + test_prep:transport_means 1 7.5 86088 3104.0
## - ethnic_group:transport_means 4 1483.7 87580 3104.1
## + test_prep:practice_sport 2 258.8 85837 3104.2
## + ethnic_group:lunch_type 4 837.4 85258 3104.3
## + transport_means:wkly_study_hours 2 238.0 85858 3104.4
## + test_prep:parent_marital_status 3 528.2 85568 3104.4
## - parent_educ:is_first_child 5 1853.3 87949 3104.6
## + practice_sport:is_first_child 2 182.2 85914 3104.8
## + gender:wkly_study_hours 2 181.4 85914 3104.8
## + practice_sport:transport_means 2 180.8 85915 3104.8
## - is_first_child:transport_means 1 780.2 86876 3105.3
## - parent_marital_status:wkly_study_hours 6 2299.8 88396 3105.6
## - parent_marital_status:transport_means 3 1462.4 87558 3106.0
## + practice_sport:wkly_study_hours 4 564.1 85532 3106.2
## + gender:parent_marital_status 3 270.0 85826 3106.2
## + parent_educ:practice_sport 10 2248.9 83847 3106.4
## + parent_educ:transport_means 5 812.6 85283 3106.4
## + lunch_type:parent_marital_status 3 221.2 85875 3106.5
## - lunch_type:practice_sport 2 1259.1 87355 3106.6
## + gender:ethnic_group 4 457.3 85638 3106.9
## + ethnic_group:test_prep 4 413.8 85682 3107.2
## + gender:parent_educ 5 671.4 85424 3107.4
## + parent_educ:lunch_type 5 584.8 85511 3108.0
## - parent_marital_status:is_first_child 3 1800.2 87896 3108.2
## - parent_educ:parent_marital_status 15 5477.3 91573 3108.4
## + parent_educ:test_prep 5 381.9 85714 3109.4
## + ethnic_group:practice_sport 8 1155.8 84940 3110.1
## + parent_marital_status:practice_sport 6 398.4 85697 3111.3
## + ethnic_group:parent_marital_status 11 1694.7 84401 3112.3
## + ethnic_group:wkly_study_hours 8 716.5 85379 3113.1
## + parent_educ:wkly_study_hours 10 1221.4 84874 3113.6
## + ethnic_group:parent_educ 20 2587.1 83509 3124.0
##
## Step: AIC=3100.31
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 67.1 86205 3098.8
## - lunch_type:is_first_child 1 87.1 86225 3098.9
## - gender:test_prep 1 125.8 86264 3099.2
## - gender:lunch_type 1 127.9 86266 3099.2
## - gender:practice_sport 2 441.0 86579 3099.3
## - lunch_type:test_prep 1 157.7 86296 3099.4
## - lunch_type:wkly_study_hours 2 527.4 86665 3099.9
## - test_prep:is_first_child 1 287.0 86425 3100.3
## <none> 86138 3100.3
## - is_first_child:wkly_study_hours 2 614.1 86752 3100.5
## - ethnic_group:is_first_child 4 1217.0 87355 3100.6
## - lunch_type:transport_means 1 350.7 86489 3100.7
## + gender:transport_means 1 42.1 86096 3102.0
## - test_prep:wkly_study_hours 2 865.7 87004 3102.2
## + test_prep:transport_means 1 10.5 86127 3102.2
## - ethnic_group:transport_means 4 1467.2 87605 3102.3
## + test_prep:practice_sport 2 254.5 85883 3102.6
## + ethnic_group:lunch_type 4 830.4 85308 3102.6
## + transport_means:wkly_study_hours 2 233.9 85904 3102.7
## + test_prep:parent_marital_status 3 517.8 85620 3102.8
## - parent_educ:is_first_child 5 1840.1 87978 3102.8
## + gender:wkly_study_hours 2 185.9 85952 3103.0
## + practice_sport:is_first_child 2 184.7 85953 3103.1
## + practice_sport:transport_means 2 182.4 85956 3103.1
## - is_first_child:transport_means 1 803.3 86941 3103.8
## - parent_marital_status:wkly_study_hours 6 2297.0 88435 3103.8
## - parent_marital_status:transport_means 3 1462.1 87600 3104.2
## + parent_educ:practice_sport 10 2282.9 83855 3104.5
## + gender:parent_marital_status 3 264.9 85873 3104.5
## + practice_sport:wkly_study_hours 4 542.5 85595 3104.6
## + parent_educ:transport_means 5 823.1 85315 3104.7
## - lunch_type:practice_sport 2 1240.0 87378 3104.8
## + lunch_type:parent_marital_status 3 222.7 85915 3104.8
## + gender:ethnic_group 4 473.5 85664 3105.1
## + ethnic_group:test_prep 4 412.7 85725 3105.5
## + gender:parent_educ 5 671.3 85467 3105.7
## + parent_educ:lunch_type 5 591.3 85547 3106.2
## - parent_educ:parent_marital_status 15 5443.9 91582 3106.5
## - parent_marital_status:is_first_child 3 1820.2 87958 3106.7
## + parent_educ:test_prep 5 385.7 85752 3107.7
## + ethnic_group:practice_sport 8 1140.5 84997 3108.4
## + parent_marital_status:practice_sport 6 390.6 85747 3109.6
## + ethnic_group:parent_marital_status 11 1717.1 84421 3110.4
## + ethnic_group:wkly_study_hours 8 709.6 85428 3111.4
## + parent_educ:wkly_study_hours 10 1196.9 84941 3112.1
## + ethnic_group:parent_educ 20 2560.8 83577 3122.5
##
## Step: AIC=3098.77
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 97.8 86303 3097.4
## - gender:test_prep 1 115.8 86321 3097.6
## - gender:lunch_type 1 127.1 86332 3097.6
## - gender:practice_sport 2 456.8 86662 3097.9
## - lunch_type:test_prep 1 169.6 86375 3097.9
## - lunch_type:wkly_study_hours 2 528.1 86733 3098.4
## <none> 86205 3098.8
## - ethnic_group:is_first_child 4 1184.1 87389 3098.8
## - test_prep:is_first_child 1 315.6 86521 3098.9
## - is_first_child:wkly_study_hours 2 648.1 86853 3099.2
## - lunch_type:transport_means 1 367.7 86573 3099.3
## + gender:is_first_child 1 67.1 86138 3100.3
## + gender:transport_means 1 41.3 86164 3100.5
## - test_prep:wkly_study_hours 2 849.9 87055 3100.6
## + test_prep:transport_means 1 10.9 86194 3100.7
## - ethnic_group:transport_means 4 1518.3 87723 3101.1
## + test_prep:practice_sport 2 241.4 85964 3101.1
## + ethnic_group:lunch_type 4 819.4 85386 3101.1
## + test_prep:parent_marital_status 3 527.3 85678 3101.2
## + transport_means:wkly_study_hours 2 221.2 85984 3101.3
## + practice_sport:transport_means 2 193.8 86011 3101.4
## + practice_sport:is_first_child 2 192.0 86013 3101.5
## + gender:wkly_study_hours 2 185.4 86020 3101.5
## - parent_educ:is_first_child 5 1889.5 88095 3101.6
## - parent_marital_status:wkly_study_hours 6 2259.4 88464 3102.0
## - is_first_child:transport_means 1 777.0 86982 3102.1
## + gender:parent_marital_status 3 287.2 85918 3102.8
## + parent_educ:practice_sport 10 2295.0 83910 3102.8
## + practice_sport:wkly_study_hours 4 562.1 85643 3102.9
## - parent_marital_status:transport_means 3 1506.1 87711 3103.0
## + parent_educ:transport_means 5 813.9 85391 3103.2
## + lunch_type:parent_marital_status 3 232.4 85973 3103.2
## + gender:ethnic_group 4 489.0 85716 3103.4
## - lunch_type:practice_sport 2 1289.5 87495 3103.5
## + ethnic_group:test_prep 4 394.8 85810 3104.1
## + gender:parent_educ 5 664.8 85540 3104.2
## + parent_educ:lunch_type 5 631.3 85574 3104.4
## - parent_educ:parent_marital_status 15 5457.7 91663 3105.0
## - parent_marital_status:is_first_child 3 1805.4 88011 3105.0
## + parent_educ:test_prep 5 387.6 85818 3106.1
## + ethnic_group:practice_sport 8 1096.1 85109 3107.2
## + parent_marital_status:practice_sport 6 389.2 85816 3108.1
## + ethnic_group:parent_marital_status 11 1738.0 84467 3108.8
## + ethnic_group:wkly_study_hours 8 685.9 85519 3110.1
## + parent_educ:wkly_study_hours 10 1203.7 85001 3110.5
## + ethnic_group:parent_educ 20 2490.6 83714 3121.5
##
## Step: AIC=3097.44
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 120.4 86423 3096.3
## - gender:test_prep 1 122.5 86425 3096.3
## - gender:practice_sport 2 425.3 86728 3096.3
## - lunch_type:test_prep 1 164.4 86467 3096.6
## - lunch_type:wkly_study_hours 2 507.0 86810 3096.9
## - ethnic_group:is_first_child 4 1131.4 87434 3097.1
## <none> 86303 3097.4
## - test_prep:is_first_child 1 293.8 86597 3097.4
## - is_first_child:wkly_study_hours 2 610.4 86913 3097.6
## - lunch_type:transport_means 1 380.8 86684 3098.0
## + lunch_type:is_first_child 1 97.8 86205 3098.8
## + gender:is_first_child 1 77.8 86225 3098.9
## + gender:transport_means 1 51.4 86251 3099.1
## - test_prep:wkly_study_hours 2 862.1 87165 3099.3
## + test_prep:transport_means 1 16.2 86287 3099.3
## + ethnic_group:lunch_type 4 823.2 85480 3099.8
## + test_prep:practice_sport 2 235.1 86068 3099.8
## + test_prep:parent_marital_status 3 520.4 85782 3099.9
## - ethnic_group:transport_means 4 1548.9 87852 3099.9
## + transport_means:wkly_study_hours 2 211.8 86091 3100.0
## + gender:wkly_study_hours 2 188.5 86114 3100.2
## + practice_sport:transport_means 2 184.2 86119 3100.2
## - parent_educ:is_first_child 5 1885.0 88188 3100.2
## + practice_sport:is_first_child 2 175.0 86128 3100.2
## - parent_marital_status:wkly_study_hours 6 2200.8 88504 3100.3
## - is_first_child:transport_means 1 770.4 87073 3100.7
## + practice_sport:wkly_study_hours 4 603.6 85699 3101.3
## + parent_educ:practice_sport 10 2322.3 83981 3101.3
## + gender:parent_marital_status 3 297.0 86006 3101.4
## - parent_marital_status:transport_means 3 1515.9 87819 3101.7
## + parent_educ:transport_means 5 822.3 85481 3101.8
## + lunch_type:parent_marital_status 3 227.7 86075 3101.9
## - lunch_type:practice_sport 2 1285.2 87588 3102.2
## + gender:ethnic_group 4 468.8 85834 3102.2
## + ethnic_group:test_prep 4 412.9 85890 3102.6
## + gender:parent_educ 5 671.5 85631 3102.8
## + parent_educ:lunch_type 5 648.6 85654 3103.0
## - parent_marital_status:is_first_child 3 1733.5 88036 3103.2
## - parent_educ:parent_marital_status 15 5422.1 91725 3103.4
## + parent_educ:test_prep 5 411.8 85891 3104.6
## + ethnic_group:practice_sport 8 1075.2 85228 3106.1
## + parent_marital_status:practice_sport 6 390.2 85913 3106.8
## + ethnic_group:parent_marital_status 11 1745.0 84558 3107.4
## + ethnic_group:wkly_study_hours 8 686.4 85616 3108.7
## + parent_educ:wkly_study_hours 10 1226.0 85077 3109.0
## + ethnic_group:parent_educ 20 2445.0 83858 3120.5
##
## Step: AIC=3096.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 108.1 86531 3095.0
## - gender:practice_sport 2 419.0 86842 3095.1
## - lunch_type:test_prep 1 190.0 86613 3095.6
## - lunch_type:wkly_study_hours 2 492.0 86915 3095.6
## - ethnic_group:is_first_child 4 1110.9 87534 3095.8
## <none> 86423 3096.3
## - test_prep:is_first_child 1 303.9 86727 3096.3
## - is_first_child:wkly_study_hours 2 606.7 87030 3096.4
## - lunch_type:transport_means 1 408.7 86832 3097.1
## + gender:lunch_type 1 120.4 86303 3097.4
## + lunch_type:is_first_child 1 91.2 86332 3097.6
## + gender:is_first_child 1 76.5 86347 3097.7
## + gender:transport_means 1 54.6 86369 3097.9
## + test_prep:transport_means 1 20.8 86403 3098.1
## - test_prep:wkly_study_hours 2 879.1 87302 3098.2
## + test_prep:practice_sport 2 250.2 86173 3098.6
## + ethnic_group:lunch_type 4 828.1 85595 3098.6
## + test_prep:parent_marital_status 3 526.2 85897 3098.7
## + transport_means:wkly_study_hours 2 200.0 86223 3098.9
## - ethnic_group:transport_means 4 1576.0 87999 3098.9
## + practice_sport:transport_means 2 181.2 86242 3099.0
## + gender:wkly_study_hours 2 166.1 86257 3099.1
## + practice_sport:is_first_child 2 161.1 86262 3099.2
## - parent_educ:is_first_child 5 1917.3 88341 3099.2
## - is_first_child:transport_means 1 743.5 87167 3099.3
## - parent_marital_status:wkly_study_hours 6 2284.1 88707 3099.7
## + practice_sport:wkly_study_hours 4 602.7 85821 3100.1
## - parent_marital_status:transport_means 3 1475.8 87899 3100.3
## + gender:parent_marital_status 3 286.4 86137 3100.3
## + parent_educ:transport_means 5 855.6 85568 3100.4
## + parent_educ:practice_sport 10 2280.1 84143 3100.5
## + lunch_type:parent_marital_status 3 258.2 86165 3100.5
## + gender:ethnic_group 4 457.4 85966 3101.1
## + ethnic_group:test_prep 4 418.7 86005 3101.4
## + parent_educ:lunch_type 5 696.7 85727 3101.5
## - lunch_type:practice_sport 2 1371.9 87795 3101.6
## - parent_marital_status:is_first_child 3 1685.0 88108 3101.7
## + gender:parent_educ 5 664.3 85759 3101.7
## - parent_educ:parent_marital_status 15 5394.8 91818 3102.0
## + parent_educ:test_prep 5 394.9 86028 3103.6
## + ethnic_group:practice_sport 8 1026.1 85397 3105.2
## + parent_marital_status:practice_sport 6 401.4 86022 3105.5
## + ethnic_group:parent_marital_status 11 1748.2 84675 3106.2
## + ethnic_group:wkly_study_hours 8 702.1 85721 3107.4
## + parent_educ:wkly_study_hours 10 1177.1 85246 3108.2
## + ethnic_group:parent_educ 20 2371.1 84052 3119.8
##
## Step: AIC=3095
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 441.2 86973 3094.0
## - ethnic_group:is_first_child 4 1074.7 87606 3094.3
## - lunch_type:test_prep 1 207.3 86739 3094.4
## - lunch_type:wkly_study_hours 2 504.2 87036 3094.4
## <none> 86531 3095.0
## - test_prep:is_first_child 1 303.6 86835 3095.1
## - is_first_child:wkly_study_hours 2 612.5 87144 3095.2
## - lunch_type:transport_means 1 426.8 86958 3095.9
## + gender:test_prep 1 108.1 86423 3096.3
## + gender:lunch_type 1 106.0 86425 3096.3
## + lunch_type:is_first_child 1 97.7 86434 3096.3
## + gender:is_first_child 1 66.6 86465 3096.6
## + gender:transport_means 1 41.4 86490 3096.7
## - test_prep:wkly_study_hours 2 845.9 87377 3096.7
## + test_prep:transport_means 1 17.0 86514 3096.9
## + ethnic_group:lunch_type 4 846.4 85685 3097.2
## + test_prep:practice_sport 2 243.1 86288 3097.3
## + test_prep:parent_marital_status 3 516.8 86015 3097.5
## - parent_educ:is_first_child 5 1876.5 88408 3097.7
## + gender:wkly_study_hours 2 188.8 86343 3097.7
## + transport_means:wkly_study_hours 2 188.1 86343 3097.7
## - ethnic_group:transport_means 4 1587.4 88119 3097.7
## + practice_sport:transport_means 2 173.6 86358 3097.8
## + practice_sport:is_first_child 2 167.8 86364 3097.9
## - is_first_child:transport_means 1 725.6 87257 3097.9
## - parent_marital_status:wkly_study_hours 6 2257.5 88789 3098.2
## + practice_sport:wkly_study_hours 4 589.5 85942 3099.0
## + gender:parent_marital_status 3 295.0 86236 3099.0
## + parent_educ:practice_sport 10 2314.6 84217 3099.0
## - parent_marital_status:transport_means 3 1496.6 88028 3099.1
## + lunch_type:parent_marital_status 3 270.6 86261 3099.2
## + parent_educ:transport_means 5 842.4 85689 3099.2
## + gender:ethnic_group 4 451.2 86080 3099.9
## - parent_marital_status:is_first_child 3 1638.4 88170 3100.1
## - lunch_type:practice_sport 2 1356.7 87888 3100.2
## + parent_educ:lunch_type 5 696.7 85835 3100.2
## + ethnic_group:test_prep 4 384.9 86146 3100.4
## - parent_educ:parent_marital_status 15 5349.4 91881 3100.4
## + gender:parent_educ 5 657.1 85874 3100.5
## + parent_educ:test_prep 5 396.0 86135 3102.3
## + parent_marital_status:practice_sport 6 425.7 86106 3104.1
## + ethnic_group:practice_sport 8 993.6 85538 3104.2
## + ethnic_group:parent_marital_status 11 1802.0 84729 3104.6
## + ethnic_group:wkly_study_hours 8 733.7 85798 3106.0
## + parent_educ:wkly_study_hours 10 1223.2 85308 3106.6
## + ethnic_group:parent_educ 20 2369.4 84162 3118.6
##
## Step: AIC=3094
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 1045.7 88018 3093.1
## - lunch_type:wkly_study_hours 2 485.3 87458 3093.3
## - lunch_type:test_prep 1 212.0 87185 3093.4
## - test_prep:is_first_child 1 279.8 87252 3093.9
## <none> 86973 3094.0
## - is_first_child:wkly_study_hours 2 618.8 87591 3094.2
## + gender:practice_sport 2 441.2 86531 3095.0
## + gender:test_prep 1 130.3 86842 3095.1
## - lunch_type:transport_means 1 467.1 87440 3095.2
## + gender:lunch_type 1 98.8 86874 3095.3
## + gender:is_first_child 1 77.3 86895 3095.5
## + lunch_type:is_first_child 1 67.1 86905 3095.6
## + gender:transport_means 1 55.4 86917 3095.6
## - test_prep:wkly_study_hours 2 847.3 87820 3095.7
## + test_prep:transport_means 1 12.9 86960 3095.9
## + test_prep:practice_sport 2 266.7 86706 3096.2
## - parent_marital_status:wkly_study_hours 6 2123.6 89096 3096.2
## + test_prep:parent_marital_status 3 531.6 86441 3096.4
## + gender:wkly_study_hours 2 221.6 86751 3096.5
## + transport_means:wkly_study_hours 2 219.6 86753 3096.5
## - ethnic_group:transport_means 4 1578.3 88551 3096.6
## - parent_educ:is_first_child 5 1897.3 88870 3096.7
## + ethnic_group:lunch_type 4 771.2 86201 3096.8
## + practice_sport:is_first_child 2 167.3 86805 3096.9
## + practice_sport:transport_means 2 155.6 86817 3096.9
## - is_first_child:transport_means 1 764.2 87737 3097.2
## - parent_marital_status:transport_means 3 1428.3 88401 3097.6
## + gender:parent_marital_status 3 346.2 86626 3097.7
## + practice_sport:wkly_study_hours 4 637.1 86335 3097.7
## + parent_educ:transport_means 5 864.0 86109 3098.1
## + lunch_type:parent_marital_status 3 267.4 86705 3098.2
## + parent_educ:practice_sport 10 2207.6 84765 3098.8
## + parent_educ:lunch_type 5 741.3 86231 3098.9
## + gender:ethnic_group 4 414.5 86558 3099.2
## - parent_educ:parent_marital_status 15 5364.1 92337 3099.3
## - parent_marital_status:is_first_child 3 1684.3 88657 3099.3
## + ethnic_group:test_prep 4 382.9 86590 3099.4
## + gender:parent_educ 5 657.1 86316 3099.5
## - lunch_type:practice_sport 2 1466.3 88439 3099.9
## + parent_educ:test_prep 5 353.3 86619 3101.6
## + ethnic_group:practice_sport 8 1131.7 85841 3102.3
## + parent_marital_status:practice_sport 6 408.6 86564 3103.2
## + ethnic_group:parent_marital_status 11 1849.7 85123 3103.3
## + ethnic_group:wkly_study_hours 8 736.7 86236 3105.0
## + parent_educ:wkly_study_hours 10 1160.6 85812 3106.1
## - gender 1 2914.0 89887 3111.4
## + ethnic_group:parent_educ 20 2455.9 84517 3117.1
##
## Step: AIC=3093.05
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:wkly_study_hours 2 439.6 88458 3092.0
## - lunch_type:test_prep 1 220.6 88239 3092.5
## <none> 88018 3093.1
## - test_prep:is_first_child 1 327.4 88346 3093.2
## - test_prep:wkly_study_hours 2 638.7 88657 3093.3
## - lunch_type:transport_means 1 406.7 88425 3093.8
## + ethnic_group:is_first_child 4 1045.7 86973 3094.0
## - is_first_child:wkly_study_hours 2 753.2 88772 3094.1
## + gender:practice_sport 2 412.2 87606 3094.3
## - is_first_child:transport_means 1 504.9 88523 3094.4
## + gender:test_prep 1 91.6 87927 3094.4
## + gender:lunch_type 1 84.2 87934 3094.5
## + gender:transport_means 1 45.0 87973 3094.8
## + gender:is_first_child 1 42.5 87976 3094.8
## - parent_marital_status:wkly_study_hours 6 2077.1 90095 3094.8
## + lunch_type:is_first_child 1 25.4 87993 3094.9
## + test_prep:transport_means 1 2.9 88015 3095.0
## + test_prep:practice_sport 2 279.7 87739 3095.2
## + test_prep:parent_marital_status 3 571.5 87447 3095.2
## + transport_means:wkly_study_hours 2 250.1 87768 3095.4
## + practice_sport:is_first_child 2 227.8 87790 3095.5
## - ethnic_group:transport_means 4 1651.1 89669 3096.0
## + gender:wkly_study_hours 2 139.5 87879 3096.1
## + practice_sport:transport_means 2 136.1 87882 3096.1
## + practice_sport:wkly_study_hours 4 699.2 87319 3096.3
## - parent_educ:is_first_child 5 2019.8 90038 3096.4
## - parent_marital_status:transport_means 3 1460.3 89479 3096.8
## + parent_educ:transport_means 5 915.0 87103 3096.9
## + gender:parent_marital_status 3 278.5 87740 3097.2
## + ethnic_group:lunch_type 4 559.4 87459 3097.3
## - parent_educ:parent_marital_status 15 5295.5 93314 3097.5
## + lunch_type:parent_marital_status 3 226.5 87792 3097.5
## + parent_educ:lunch_type 5 815.5 87203 3097.6
## + parent_educ:practice_sport 10 2279.3 85739 3097.6
## + ethnic_group:test_prep 4 411.9 87606 3098.3
## - lunch_type:practice_sport 2 1396.6 89415 3098.3
## + gender:ethnic_group 4 377.8 87641 3098.5
## - parent_marital_status:is_first_child 3 1836.6 89855 3099.2
## + gender:parent_educ 5 561.0 87457 3099.3
## + parent_educ:test_prep 5 377.5 87641 3100.5
## + ethnic_group:practice_sport 8 1053.2 86965 3101.9
## + parent_marital_status:practice_sport 6 283.5 87735 3103.2
## + ethnic_group:wkly_study_hours 8 783.8 87235 3103.8
## + ethnic_group:parent_marital_status 11 1528.1 86490 3104.7
## + parent_educ:wkly_study_hours 10 1203.3 86815 3104.9
## - gender 1 3194.3 91213 3112.1
## + ethnic_group:parent_educ 20 2547.3 85471 3115.7
##
## Step: AIC=3091.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 183.8 88642 3091.2
## <none> 88458 3092.0
## - test_prep:is_first_child 1 353.8 88812 3092.3
## - lunch_type:transport_means 1 389.2 88847 3092.6
## - test_prep:wkly_study_hours 2 693.4 89151 3092.6
## - parent_marital_status:wkly_study_hours 6 1937.5 90395 3092.8
## + lunch_type:wkly_study_hours 2 439.6 88018 3093.1
## - is_first_child:wkly_study_hours 2 763.2 89221 3093.1
## + ethnic_group:is_first_child 4 1000.0 87458 3093.3
## + gender:test_prep 1 103.6 88354 3093.3
## + gender:practice_sport 2 395.2 88063 3093.3
## + gender:lunch_type 1 74.0 88384 3093.5
## - is_first_child:transport_means 1 556.8 89015 3093.7
## + gender:is_first_child 1 40.5 88417 3093.7
## + gender:transport_means 1 29.5 88428 3093.8
## + test_prep:practice_sport 2 322.7 88135 3093.8
## + lunch_type:is_first_child 1 16.5 88441 3093.9
## + test_prep:transport_means 1 1.5 88456 3094.0
## + transport_means:wkly_study_hours 2 289.0 88169 3094.1
## + test_prep:parent_marital_status 3 573.8 87884 3094.2
## + practice_sport:is_first_child 2 234.2 88224 3094.4
## - ethnic_group:transport_means 4 1593.9 90052 3094.5
## - parent_educ:is_first_child 5 1983.0 90441 3095.1
## + practice_sport:transport_means 2 128.9 88329 3095.1
## + gender:wkly_study_hours 2 103.0 88355 3095.3
## + parent_educ:transport_means 5 988.3 87470 3095.4
## - parent_marital_status:transport_means 3 1439.2 89897 3095.5
## + practice_sport:wkly_study_hours 4 664.7 87793 3095.5
## + gender:parent_marital_status 3 332.0 88126 3095.8
## + parent_educ:practice_sport 10 2350.0 86108 3096.1
## + lunch_type:parent_marital_status 3 206.8 88251 3096.6
## + ethnic_group:lunch_type 4 504.4 87953 3096.6
## - parent_educ:parent_marital_status 15 5358.7 93817 3096.7
## + ethnic_group:test_prep 4 423.2 88035 3097.2
## + parent_educ:lunch_type 5 709.1 87749 3097.2
## - lunch_type:practice_sport 2 1411.9 89870 3097.3
## + gender:ethnic_group 4 346.1 88112 3097.7
## + gender:parent_educ 5 616.5 87841 3097.9
## - parent_marital_status:is_first_child 3 1837.0 90295 3098.1
## + parent_educ:test_prep 5 386.1 88072 3099.4
## + ethnic_group:practice_sport 8 1034.5 87423 3101.1
## + parent_marital_status:practice_sport 6 290.1 88168 3102.1
## + ethnic_group:wkly_study_hours 8 803.7 87654 3102.6
## + ethnic_group:parent_marital_status 11 1478.6 86979 3104.1
## + parent_educ:wkly_study_hours 10 1132.5 87325 3104.4
## - gender 1 3238.9 91697 3111.2
## + ethnic_group:parent_educ 20 2566.2 85892 3114.6
##
## Step: AIC=3091.22
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 88642 3091.2
## - test_prep:is_first_child 1 340.8 88982 3091.5
## - lunch_type:transport_means 1 343.0 88985 3091.5
## - test_prep:wkly_study_hours 2 699.0 89341 3091.8
## + lunch_type:test_prep 1 183.8 88458 3092.0
## - parent_marital_status:wkly_study_hours 6 1959.2 90601 3092.1
## + gender:test_prep 1 118.0 88524 3092.4
## + ethnic_group:is_first_child 4 1007.9 87634 3092.5
## + lunch_type:wkly_study_hours 2 402.8 88239 3092.5
## + gender:practice_sport 2 399.7 88242 3092.6
## - is_first_child:wkly_study_hours 2 806.1 89448 3092.6
## - is_first_child:transport_means 1 504.9 89147 3092.6
## + gender:lunch_type 1 94.2 88547 3092.6
## + gender:is_first_child 1 46.8 88595 3092.9
## + gender:transport_means 1 33.6 88608 3093.0
## + test_prep:practice_sport 2 332.6 88309 3093.0
## + lunch_type:is_first_child 1 14.2 88627 3093.1
## + test_prep:transport_means 1 0.9 88641 3093.2
## + test_prep:parent_marital_status 3 572.8 88069 3093.4
## + transport_means:wkly_study_hours 2 262.7 88379 3093.5
## + practice_sport:is_first_child 2 245.6 88396 3093.6
## - ethnic_group:transport_means 4 1620.7 90262 3093.9
## - parent_educ:is_first_child 5 1937.1 90579 3094.0
## + practice_sport:transport_means 2 152.2 88490 3094.2
## + gender:wkly_study_hours 2 104.4 88537 3094.5
## + practice_sport:wkly_study_hours 4 694.6 87947 3094.6
## + parent_educ:transport_means 5 980.6 87661 3094.7
## - parent_marital_status:transport_means 3 1457.2 90099 3094.8
## + gender:parent_marital_status 3 336.0 88306 3095.0
## - parent_educ:parent_marital_status 15 5267.7 93909 3095.3
## + parent_educ:practice_sport 10 2356.5 86285 3095.3
## + ethnic_group:lunch_type 4 527.6 88114 3095.7
## + lunch_type:parent_marital_status 3 190.8 88451 3095.9
## - lunch_type:practice_sport 2 1378.2 90020 3096.3
## + ethnic_group:test_prep 4 405.7 88236 3096.5
## + parent_educ:lunch_type 5 676.9 87965 3096.7
## + gender:ethnic_group 4 349.9 88292 3096.9
## + gender:parent_educ 5 646.5 87995 3096.9
## - parent_marital_status:is_first_child 3 1860.2 90502 3097.5
## + parent_educ:test_prep 5 412.2 88229 3098.5
## + ethnic_group:practice_sport 8 1081.3 87560 3100.0
## + parent_marital_status:practice_sport 6 299.4 88342 3101.2
## + ethnic_group:wkly_study_hours 8 857.1 87785 3101.5
## + parent_educ:wkly_study_hours 10 1206.0 87436 3103.1
## + ethnic_group:parent_marital_status 11 1444.1 87198 3103.5
## - gender 1 3294.9 91937 3110.8
## + ethnic_group:parent_educ 20 2571.4 86070 3113.8summary(stepwise_model_math)##
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## lunch_type:practice_sport + lunch_type:transport_means +
## test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours,
## data = df_4_mdl_math)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.225 -8.356 0.435 8.408 29.970
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 43.4922 7.6094
## gendermale 5.0562 1.1468
## ethnic_groupgroup B 3.1099 3.8855
## ethnic_groupgroup C 4.7867 3.5363
## ethnic_groupgroup D 4.4789 3.6141
## ethnic_groupgroup E 19.5605 4.0197
## parent_educbachelor's degree 22.6142 6.3793
## parent_educhigh school -11.9676 5.2257
## parent_educmaster's degree -1.9384 7.3940
## parent_educsome college 0.8824 5.2535
## parent_educsome high school 1.6696 5.2602
## lunch_typestandard 5.7052 3.8861
## test_prepnone -1.1067 3.0821
## parent_marital_statusmarried 9.7202 5.4642
## parent_marital_statussingle 3.7791 6.1207
## parent_marital_statuswidowed 29.2538 21.3074
## practice_sportregularly -4.2709 3.3825
## practice_sportsometimes -6.0415 3.2607
## is_first_childyes 12.5726 5.4684
## transport_meansschool_bus 5.2495 5.3829
## wkly_study_hours> 10 -4.8803 6.2686
## wkly_study_hours10-May 4.6584 4.6603
## ethnic_groupgroup B:transport_meansschool_bus -4.3677 4.8098
## ethnic_groupgroup C:transport_meansschool_bus -7.7457 4.4977
## ethnic_groupgroup D:transport_meansschool_bus -0.9133 4.5777
## ethnic_groupgroup E:transport_meansschool_bus -10.3518 5.0390
## parent_educbachelor's degree:parent_marital_statusmarried -18.4745 6.5736
## parent_educhigh school:parent_marital_statusmarried 0.7418 4.8751
## parent_educmaster's degree:parent_marital_statusmarried 1.1993 6.6521
## parent_educsome college:parent_marital_statusmarried -7.4232 4.9354
## parent_educsome high school:parent_marital_statusmarried -8.2283 4.9536
## parent_educbachelor's degree:parent_marital_statussingle -23.6304 7.4269
## parent_educhigh school:parent_marital_statussingle 1.7141 5.5986
## parent_educmaster's degree:parent_marital_statussingle -0.6344 7.3500
## parent_educsome college:parent_marital_statussingle -11.5881 5.6728
## parent_educsome high school:parent_marital_statussingle -11.5407 5.5591
## parent_educbachelor's degree:parent_marital_statuswidowed -33.5004 17.3280
## parent_educhigh school:parent_marital_statuswidowed -46.5554 20.4448
## parent_educmaster's degree:parent_marital_statuswidowed -48.9590 29.6690
## parent_educsome college:parent_marital_statuswidowed -15.7099 19.0668
## parent_educsome high school:parent_marital_statuswidowed -19.2638 19.6446
## parent_educbachelor's degree:is_first_childyes -3.3589 4.3330
## parent_educhigh school:is_first_childyes 8.9969 3.8002
## parent_educmaster's degree:is_first_childyes 4.7183 5.6364
## parent_educsome college:is_first_childyes 6.6947 3.7542
## parent_educsome high school:is_first_childyes 2.0436 3.7438
## lunch_typestandard:practice_sportregularly 8.4203 4.1608
## lunch_typestandard:practice_sportsometimes 11.3662 4.0244
## lunch_typestandard:transport_meansschool_bus -3.4368 2.4159
## test_prepnone:is_first_childyes -3.6884 2.6012
## test_prepnone:wkly_study_hours> 10 -6.2865 3.6457
## test_prepnone:wkly_study_hours10-May -0.1976 2.8984
## parent_marital_statusmarried:is_first_childyes -8.7047 3.9485
## parent_marital_statussingle:is_first_childyes -1.9060 4.3893
## parent_marital_statuswidowed:is_first_childyes 13.7975 13.4714
## parent_marital_statusmarried:transport_meansschool_bus 7.2707 3.3639
## parent_marital_statussingle:transport_meansschool_bus 2.4715 3.7983
## parent_marital_statuswidowed:transport_meansschool_bus -14.6085 12.8542
## parent_marital_statusmarried:wkly_study_hours> 10 11.6354 5.1480
## parent_marital_statussingle:wkly_study_hours> 10 18.6339 5.7474
## parent_marital_statuswidowed:wkly_study_hours> 10 11.9898 16.7894
## parent_marital_statusmarried:wkly_study_hours10-May 2.1127 3.7866
## parent_marital_statussingle:wkly_study_hours10-May 5.6965 4.2936
## parent_marital_statuswidowed:wkly_study_hours10-May 11.8849 14.3211
## is_first_childyes:transport_meansschool_bus -4.4000 2.5494
## is_first_childyes:wkly_study_hours> 10 -0.6479 3.7705
## is_first_childyes:wkly_study_hours10-May -5.6646 2.8793
## t value Pr(>|t|)
## (Intercept) 5.716 1.84e-08 ***
## gendermale 4.409 1.26e-05 ***
## ethnic_groupgroup B 0.800 0.423863
## ethnic_groupgroup C 1.354 0.176457
## ethnic_groupgroup D 1.239 0.215799
## ethnic_groupgroup E 4.866 1.51e-06 ***
## parent_educbachelor's degree 3.545 0.000428 ***
## parent_educhigh school -2.290 0.022411 *
## parent_educmaster's degree -0.262 0.793302
## parent_educsome college 0.168 0.866672
## parent_educsome high school 0.317 0.751071
## lunch_typestandard 1.468 0.142671
## test_prepnone -0.359 0.719670
## parent_marital_statusmarried 1.779 0.075838 .
## parent_marital_statussingle 0.617 0.537217
## parent_marital_statuswidowed 1.373 0.170360
## practice_sportregularly -1.263 0.207275
## practice_sportsometimes -1.853 0.064470 .
## is_first_childyes 2.299 0.021890 *
## transport_meansschool_bus 0.975 0.329901
## wkly_study_hours> 10 -0.779 0.436602
## wkly_study_hours10-May 1.000 0.317963
## ethnic_groupgroup B:transport_meansschool_bus -0.908 0.364253
## ethnic_groupgroup C:transport_meansschool_bus -1.722 0.085632 .
## ethnic_groupgroup D:transport_meansschool_bus -0.200 0.841936
## ethnic_groupgroup E:transport_meansschool_bus -2.054 0.040440 *
## parent_educbachelor's degree:parent_marital_statusmarried -2.810 0.005133 **
## parent_educhigh school:parent_marital_statusmarried 0.152 0.879115
## parent_educmaster's degree:parent_marital_statusmarried 0.180 0.856998
## parent_educsome college:parent_marital_statusmarried -1.504 0.133168
## parent_educsome high school:parent_marital_statusmarried -1.661 0.097298 .
## parent_educbachelor's degree:parent_marital_statussingle -3.182 0.001551 **
## parent_educhigh school:parent_marital_statussingle 0.306 0.759606
## parent_educmaster's degree:parent_marital_statussingle -0.086 0.931250
## parent_educsome college:parent_marital_statussingle -2.043 0.041580 *
## parent_educsome high school:parent_marital_statussingle -2.076 0.038380 *
## parent_educbachelor's degree:parent_marital_statuswidowed -1.933 0.053737 .
## parent_educhigh school:parent_marital_statuswidowed -2.277 0.023182 *
## parent_educmaster's degree:parent_marital_statuswidowed -1.650 0.099508 .
## parent_educsome college:parent_marital_statuswidowed -0.824 0.410350
## parent_educsome high school:parent_marital_statuswidowed -0.981 0.327238
## parent_educbachelor's degree:is_first_childyes -0.775 0.438573
## parent_educhigh school:is_first_childyes 2.368 0.018271 *
## parent_educmaster's degree:is_first_childyes 0.837 0.402905
## parent_educsome college:is_first_childyes 1.783 0.075121 .
## parent_educsome high school:is_first_childyes 0.546 0.585404
## lunch_typestandard:practice_sportregularly 2.024 0.043509 *
## lunch_typestandard:practice_sportsometimes 2.824 0.004918 **
## lunch_typestandard:transport_meansschool_bus -1.423 0.155457
## test_prepnone:is_first_childyes -1.418 0.156801
## test_prepnone:wkly_study_hours> 10 -1.724 0.085236 .
## test_prepnone:wkly_study_hours10-May -0.068 0.945661
## parent_marital_statusmarried:is_first_childyes -2.205 0.027922 *
## parent_marital_statussingle:is_first_childyes -0.434 0.664285
## parent_marital_statuswidowed:is_first_childyes 1.024 0.306211
## parent_marital_statusmarried:transport_meansschool_bus 2.161 0.031117 *
## parent_marital_statussingle:transport_meansschool_bus 0.651 0.515535
## parent_marital_statuswidowed:transport_meansschool_bus -1.136 0.256279
## parent_marital_statusmarried:wkly_study_hours> 10 2.260 0.024220 *
## parent_marital_statussingle:wkly_study_hours> 10 3.242 0.001262 **
## parent_marital_statuswidowed:wkly_study_hours> 10 0.714 0.475465
## parent_marital_statusmarried:wkly_study_hours10-May 0.558 0.577124
## parent_marital_statussingle:wkly_study_hours10-May 1.327 0.185170
## parent_marital_statuswidowed:wkly_study_hours10-May 0.830 0.406980
## is_first_childyes:transport_meansschool_bus -1.726 0.084951 .
## is_first_childyes:wkly_study_hours> 10 -0.172 0.863627
## is_first_childyes:wkly_study_hours10-May -1.967 0.049669 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.02 on 523 degrees of freedom
## Multiple R-squared: 0.4207, Adjusted R-squared: 0.3476
## F-statistic: 5.755 on 66 and 523 DF, p-value: < 2.2e-16REading Score
df_4_mdl_read=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score)
full_fit_read=lm(reading_score ~ .^2,data=df_4_mdl_read)summary(full_fit_read)##
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.758 -7.294 0.000 7.418 27.742
##
## Coefficients: (4 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 81.321731 17.167189
## gendermale -12.452051 8.746220
## ethnic_groupgroup B -22.239861 14.760619
## ethnic_groupgroup C -29.866442 13.925159
## ethnic_groupgroup D -14.526414 15.158345
## ethnic_groupgroup E -12.302699 14.206212
## parent_educbachelor's degree 33.009059 15.519735
## parent_educhigh school 10.568006 12.847471
## parent_educmaster's degree -24.461817 21.208891
## parent_educsome college -8.316968 12.606066
## parent_educsome high school -4.455992 12.227987
## lunch_typestandard 2.962788 8.683223
## test_prepnone -21.345506 9.059903
## parent_marital_statusmarried 16.095657 11.535602
## parent_marital_statussingle 5.120602 13.883607
## parent_marital_statuswidowed 30.884374 41.015667
## practice_sportregularly -22.428022 13.810663
## practice_sportsometimes -19.634669 13.740867
## is_first_childyes 16.375726 9.948217
## transport_meansschool_bus -1.212990 8.806349
## wkly_study_hours> 10 -17.887902 13.565927
## wkly_study_hours10-May 6.195369 10.901941
## gendermale:ethnic_groupgroup B 7.922999 5.540120
## gendermale:ethnic_groupgroup C 12.191147 5.327795
## gendermale:ethnic_groupgroup D 8.192752 5.292503
## gendermale:ethnic_groupgroup E 9.251399 5.868168
## gendermale:parent_educbachelor's degree -2.815989 4.660163
## gendermale:parent_educhigh school 0.610374 3.800446
## gendermale:parent_educmaster's degree 7.279615 6.524814
## gendermale:parent_educsome college -4.141922 3.991004
## gendermale:parent_educsome high school 1.008352 3.920233
## gendermale:lunch_typestandard -1.073739 2.722340
## gendermale:test_prepnone 0.251653 2.713118
## gendermale:parent_marital_statusmarried -0.523193 3.867655
## gendermale:parent_marital_statussingle -1.745302 4.384747
## gendermale:parent_marital_statuswidowed 1.627846 18.986441
## gendermale:practice_sportregularly -4.310235 4.610325
## gendermale:practice_sportsometimes -3.516087 4.634508
## gendermale:is_first_childyes 3.360372 2.847909
## gendermale:transport_meansschool_bus -0.351231 2.632552
## gendermale:wkly_study_hours> 10 -4.536157 4.129918
## gendermale:wkly_study_hours10-May -1.585990 3.132127
## ethnic_groupgroup B:parent_educbachelor's degree -3.324954 12.924044
## ethnic_groupgroup C:parent_educbachelor's degree -1.783597 12.903276
## ethnic_groupgroup D:parent_educbachelor's degree -4.193155 12.805839
## ethnic_groupgroup E:parent_educbachelor's degree -11.352581 14.573901
## ethnic_groupgroup B:parent_educhigh school -15.455925 8.091351
## ethnic_groupgroup C:parent_educhigh school -8.942855 7.776991
## ethnic_groupgroup D:parent_educhigh school -7.859495 7.906714
## ethnic_groupgroup E:parent_educhigh school -9.368700 8.805485
## ethnic_groupgroup B:parent_educmaster's degree 19.405920 15.527488
## ethnic_groupgroup C:parent_educmaster's degree 4.673731 14.422492
## ethnic_groupgroup D:parent_educmaster's degree 12.168775 14.651954
## ethnic_groupgroup E:parent_educmaster's degree 14.049007 15.416565
## ethnic_groupgroup B:parent_educsome college 4.664900 8.948253
## ethnic_groupgroup C:parent_educsome college 8.349426 8.446297
## ethnic_groupgroup D:parent_educsome college 11.079460 8.797228
## ethnic_groupgroup E:parent_educsome college 8.211551 8.893668
## ethnic_groupgroup B:parent_educsome high school -11.966506 8.576569
## ethnic_groupgroup C:parent_educsome high school -4.495760 8.047085
## ethnic_groupgroup D:parent_educsome high school -3.780939 8.099992
## ethnic_groupgroup E:parent_educsome high school 4.417092 8.696931
## ethnic_groupgroup B:lunch_typestandard 5.652071 5.760897
## ethnic_groupgroup C:lunch_typestandard 10.226437 5.587239
## ethnic_groupgroup D:lunch_typestandard 8.972876 5.499776
## ethnic_groupgroup E:lunch_typestandard 1.828807 6.373559
## ethnic_groupgroup B:test_prepnone 5.358082 5.877498
## ethnic_groupgroup C:test_prepnone 10.226148 5.513504
## ethnic_groupgroup D:test_prepnone 7.509603 5.524539
## ethnic_groupgroup E:test_prepnone 13.877806 6.013663
## ethnic_groupgroup B:parent_marital_statusmarried 7.666966 7.934987
## ethnic_groupgroup C:parent_marital_statusmarried 1.502948 7.306752
## ethnic_groupgroup D:parent_marital_statusmarried -9.884703 7.206665
## ethnic_groupgroup E:parent_marital_statusmarried -0.914626 7.973170
## ethnic_groupgroup B:parent_marital_statussingle 18.560281 9.394771
## ethnic_groupgroup C:parent_marital_statussingle 7.986241 8.882343
## ethnic_groupgroup D:parent_marital_statussingle 3.213487 8.582960
## ethnic_groupgroup E:parent_marital_statussingle 14.967904 9.892795
## ethnic_groupgroup B:parent_marital_statuswidowed 50.612530 105.115426
## ethnic_groupgroup C:parent_marital_statuswidowed 78.991045 85.429965
## ethnic_groupgroup D:parent_marital_statuswidowed 4.650894 86.120208
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 14.613295 10.525698
## ethnic_groupgroup C:practice_sportregularly 14.627286 10.430812
## ethnic_groupgroup D:practice_sportregularly 12.114331 11.643524
## ethnic_groupgroup E:practice_sportregularly 15.486520 10.659168
## ethnic_groupgroup B:practice_sportsometimes 14.385211 11.228160
## ethnic_groupgroup C:practice_sportsometimes 22.578975 10.921110
## ethnic_groupgroup D:practice_sportsometimes 13.257823 12.039573
## ethnic_groupgroup E:practice_sportsometimes 14.799736 10.976620
## ethnic_groupgroup B:is_first_childyes 7.019423 5.832717
## ethnic_groupgroup C:is_first_childyes 0.945600 5.502186
## ethnic_groupgroup D:is_first_childyes -0.578091 5.565974
## ethnic_groupgroup E:is_first_childyes 0.006724 6.269137
## ethnic_groupgroup B:transport_meansschool_bus -9.549492 5.835934
## ethnic_groupgroup C:transport_meansschool_bus -12.156811 5.388780
## ethnic_groupgroup D:transport_meansschool_bus -3.839999 5.383422
## ethnic_groupgroup E:transport_meansschool_bus -11.722753 6.354914
## ethnic_groupgroup B:wkly_study_hours> 10 -8.400227 9.935104
## ethnic_groupgroup C:wkly_study_hours> 10 -0.687654 9.811241
## ethnic_groupgroup D:wkly_study_hours> 10 0.263262 9.797612
## ethnic_groupgroup E:wkly_study_hours> 10 -2.759617 10.673194
## ethnic_groupgroup B:wkly_study_hours10-May -7.860645 8.344055
## ethnic_groupgroup C:wkly_study_hours10-May -2.433650 8.164758
## ethnic_groupgroup D:wkly_study_hours10-May -2.347630 8.302701
## ethnic_groupgroup E:wkly_study_hours10-May -6.220986 8.939387
## parent_educbachelor's degree:lunch_typestandard 0.537231 5.014512
## parent_educhigh school:lunch_typestandard 0.798236 4.046623
## parent_educmaster's degree:lunch_typestandard 6.644511 7.416722
## parent_educsome college:lunch_typestandard 3.328751 4.079308
## parent_educsome high school:lunch_typestandard 5.530921 4.225656
## parent_educbachelor's degree:test_prepnone -2.906807 4.626773
## parent_educhigh school:test_prepnone 2.313360 4.431222
## parent_educmaster's degree:test_prepnone 0.511485 7.888189
## parent_educsome college:test_prepnone -3.095198 4.153258
## parent_educsome high school:test_prepnone 2.618495 4.016780
## parent_educbachelor's degree:parent_marital_statusmarried -18.253458 8.257834
## parent_educhigh school:parent_marital_statusmarried 3.996656 5.807660
## parent_educmaster's degree:parent_marital_statusmarried 0.758405 8.402414
## parent_educsome college:parent_marital_statusmarried -7.340772 5.719024
## parent_educsome high school:parent_marital_statusmarried -4.263094 5.636000
## parent_educbachelor's degree:parent_marital_statussingle -16.758528 8.901756
## parent_educhigh school:parent_marital_statussingle 8.616682 6.344144
## parent_educmaster's degree:parent_marital_statussingle 0.012577 8.969310
## parent_educsome college:parent_marital_statussingle -5.727081 6.369453
## parent_educsome high school:parent_marital_statussingle -1.033222 6.292098
## parent_educbachelor's degree:parent_marital_statuswidowed -21.688307 87.516115
## parent_educhigh school:parent_marital_statuswidowed -57.550419 96.291731
## parent_educmaster's degree:parent_marital_statuswidowed -77.367781 50.441787
## parent_educsome college:parent_marital_statuswidowed -60.045162 63.244771
## parent_educsome high school:parent_marital_statuswidowed -37.108747 75.801849
## parent_educbachelor's degree:practice_sportregularly -3.662981 8.525723
## parent_educhigh school:practice_sportregularly -14.710426 7.337095
## parent_educmaster's degree:practice_sportregularly 1.377177 10.367956
## parent_educsome college:practice_sportregularly -0.382685 7.461303
## parent_educsome high school:practice_sportregularly -3.964045 7.205456
## parent_educbachelor's degree:practice_sportsometimes -12.591005 8.181090
## parent_educhigh school:practice_sportsometimes -11.930485 6.949111
## parent_educmaster's degree:practice_sportsometimes 6.527368 8.636835
## parent_educsome college:practice_sportsometimes 1.040653 7.180635
## parent_educsome high school:practice_sportsometimes 1.496483 6.751679
## parent_educbachelor's degree:is_first_childyes 4.788458 5.062901
## parent_educhigh school:is_first_childyes 6.532806 4.321769
## parent_educmaster's degree:is_first_childyes 6.212508 7.559206
## parent_educsome college:is_first_childyes 9.548352 4.220353
## parent_educsome high school:is_first_childyes 4.792705 4.250326
## parent_educbachelor's degree:transport_meansschool_bus 0.906739 5.054249
## parent_educhigh school:transport_meansschool_bus 3.388782 4.035129
## parent_educmaster's degree:transport_meansschool_bus 4.816803 6.221602
## parent_educsome college:transport_meansschool_bus 3.654650 4.108899
## parent_educsome high school:transport_meansschool_bus 6.032445 4.180954
## parent_educbachelor's degree:wkly_study_hours> 10 -8.191880 7.456993
## parent_educhigh school:wkly_study_hours> 10 -8.343145 6.207418
## parent_educmaster's degree:wkly_study_hours> 10 -1.790263 13.431842
## parent_educsome college:wkly_study_hours> 10 -5.998216 6.248173
## parent_educsome high school:wkly_study_hours> 10 -6.744473 6.363801
## parent_educbachelor's degree:wkly_study_hours10-May -1.946279 5.182903
## parent_educhigh school:wkly_study_hours10-May -10.690295 4.832196
## parent_educmaster's degree:wkly_study_hours10-May -1.124984 6.910172
## parent_educsome college:wkly_study_hours10-May -2.915727 4.920451
## parent_educsome high school:wkly_study_hours10-May -8.675554 5.191456
## lunch_typestandard:test_prepnone -3.365201 3.035153
## lunch_typestandard:parent_marital_statusmarried -7.902908 3.971499
## lunch_typestandard:parent_marital_statussingle -3.707488 4.598623
## lunch_typestandard:parent_marital_statuswidowed 9.372773 78.604395
## lunch_typestandard:practice_sportregularly 6.988929 5.235054
## lunch_typestandard:practice_sportsometimes 10.284128 5.046396
## lunch_typestandard:is_first_childyes -3.701755 3.075286
## lunch_typestandard:transport_meansschool_bus -3.696061 2.822109
## lunch_typestandard:wkly_study_hours> 10 7.910873 4.306472
## lunch_typestandard:wkly_study_hours10-May -0.616925 3.221350
## test_prepnone:parent_marital_statusmarried 3.767046 4.039735
## test_prepnone:parent_marital_statussingle -0.269557 4.650957
## test_prepnone:parent_marital_statuswidowed -33.676919 41.067330
## test_prepnone:practice_sportregularly 2.975412 5.049660
## test_prepnone:practice_sportsometimes 4.627924 4.948802
## test_prepnone:is_first_childyes 1.185331 3.047862
## test_prepnone:transport_meansschool_bus 1.799887 2.771281
## test_prepnone:wkly_study_hours> 10 -2.777623 4.350100
## test_prepnone:wkly_study_hours10-May 1.550628 3.433108
## parent_marital_statusmarried:practice_sportregularly 3.293520 6.491421
## parent_marital_statussingle:practice_sportregularly -4.424243 8.489011
## parent_marital_statuswidowed:practice_sportregularly -6.906882 83.123661
## parent_marital_statusmarried:practice_sportsometimes 1.290178 6.401773
## parent_marital_statussingle:practice_sportsometimes -4.334220 8.299021
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -17.146416 4.775198
## parent_marital_statussingle:is_first_childyes -8.538880 5.292427
## parent_marital_statuswidowed:is_first_childyes 21.917582 29.457760
## parent_marital_statusmarried:transport_meansschool_bus 4.369244 3.943480
## parent_marital_statussingle:transport_meansschool_bus -1.084605 4.494112
## parent_marital_statuswidowed:transport_meansschool_bus -14.288412 19.143923
## parent_marital_statusmarried:wkly_study_hours> 10 21.137631 6.160491
## parent_marital_statussingle:wkly_study_hours> 10 27.104463 6.851117
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 3.638193 4.522464
## parent_marital_statussingle:wkly_study_hours10-May 4.406511 4.994941
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -3.848217 5.864087
## practice_sportsometimes:is_first_childyes -6.246496 5.721937
## practice_sportregularly:transport_meansschool_bus 8.897678 4.900075
## practice_sportsometimes:transport_meansschool_bus 5.610130 4.755946
## practice_sportregularly:wkly_study_hours> 10 4.200015 6.947009
## practice_sportsometimes:wkly_study_hours> 10 3.936511 6.813953
## practice_sportregularly:wkly_study_hours10-May 7.801823 5.346218
## practice_sportsometimes:wkly_study_hours10-May 0.374090 5.271160
## is_first_childyes:transport_meansschool_bus -1.537098 2.982819
## is_first_childyes:wkly_study_hours> 10 2.206912 4.484172
## is_first_childyes:wkly_study_hours10-May -2.954512 3.384923
## transport_meansschool_bus:wkly_study_hours> 10 0.704788 4.309112
## transport_meansschool_bus:wkly_study_hours10-May 2.548938 3.111517
## t value Pr(>|t|)
## (Intercept) 4.737 3.06e-06 ***
## gendermale -1.424 0.155346
## ethnic_groupgroup B -1.507 0.132711
## ethnic_groupgroup C -2.145 0.032599 *
## ethnic_groupgroup D -0.958 0.338510
## ethnic_groupgroup E -0.866 0.387028
## parent_educbachelor's degree 2.127 0.034066 *
## parent_educhigh school 0.823 0.411262
## parent_educmaster's degree -1.153 0.249476
## parent_educsome college -0.660 0.509805
## parent_educsome high school -0.364 0.715753
## lunch_typestandard 0.341 0.733134
## test_prepnone -2.356 0.018974 *
## parent_marital_statusmarried 1.395 0.163733
## parent_marital_statussingle 0.369 0.712463
## parent_marital_statuswidowed 0.753 0.451919
## practice_sportregularly -1.624 0.105206
## practice_sportsometimes -1.429 0.153841
## is_first_childyes 1.646 0.100564
## transport_meansschool_bus -0.138 0.890518
## wkly_study_hours> 10 -1.319 0.188094
## wkly_study_hours10-May 0.568 0.570177
## gendermale:ethnic_groupgroup B 1.430 0.153500
## gendermale:ethnic_groupgroup C 2.288 0.022669 *
## gendermale:ethnic_groupgroup D 1.548 0.122450
## gendermale:ethnic_groupgroup E 1.577 0.115727
## gendermale:parent_educbachelor's degree -0.604 0.546023
## gendermale:parent_educhigh school 0.161 0.872488
## gendermale:parent_educmaster's degree 1.116 0.265258
## gendermale:parent_educsome college -1.038 0.300011
## gendermale:parent_educsome high school 0.257 0.797149
## gendermale:lunch_typestandard -0.394 0.693492
## gendermale:test_prepnone 0.093 0.926147
## gendermale:parent_marital_statusmarried -0.135 0.892466
## gendermale:parent_marital_statussingle -0.398 0.690823
## gendermale:parent_marital_statuswidowed 0.086 0.931720
## gendermale:practice_sportregularly -0.935 0.350424
## gendermale:practice_sportsometimes -0.759 0.448513
## gendermale:is_first_childyes 1.180 0.238755
## gendermale:transport_meansschool_bus -0.133 0.893933
## gendermale:wkly_study_hours> 10 -1.098 0.272735
## gendermale:wkly_study_hours10-May -0.506 0.612894
## ethnic_groupgroup B:parent_educbachelor's degree -0.257 0.797109
## ethnic_groupgroup C:parent_educbachelor's degree -0.138 0.890133
## ethnic_groupgroup D:parent_educbachelor's degree -0.327 0.743513
## ethnic_groupgroup E:parent_educbachelor's degree -0.779 0.436480
## ethnic_groupgroup B:parent_educhigh school -1.910 0.056857 .
## ethnic_groupgroup C:parent_educhigh school -1.150 0.250898
## ethnic_groupgroup D:parent_educhigh school -0.994 0.320837
## ethnic_groupgroup E:parent_educhigh school -1.064 0.288016
## ethnic_groupgroup B:parent_educmaster's degree 1.250 0.212144
## ethnic_groupgroup C:parent_educmaster's degree 0.324 0.746071
## ethnic_groupgroup D:parent_educmaster's degree 0.831 0.406761
## ethnic_groupgroup E:parent_educmaster's degree 0.911 0.362714
## ethnic_groupgroup B:parent_educsome college 0.521 0.602445
## ethnic_groupgroup C:parent_educsome college 0.989 0.323517
## ethnic_groupgroup D:parent_educsome college 1.259 0.208643
## ethnic_groupgroup E:parent_educsome college 0.923 0.356431
## ethnic_groupgroup B:parent_educsome high school -1.395 0.163747
## ethnic_groupgroup C:parent_educsome high school -0.559 0.576705
## ethnic_groupgroup D:parent_educsome high school -0.467 0.640921
## ethnic_groupgroup E:parent_educsome high school 0.508 0.611822
## ethnic_groupgroup B:lunch_typestandard 0.981 0.327158
## ethnic_groupgroup C:lunch_typestandard 1.830 0.067979 .
## ethnic_groupgroup D:lunch_typestandard 1.631 0.103607
## ethnic_groupgroup E:lunch_typestandard 0.287 0.774316
## ethnic_groupgroup B:test_prepnone 0.912 0.362539
## ethnic_groupgroup C:test_prepnone 1.855 0.064401 .
## ethnic_groupgroup D:test_prepnone 1.359 0.174846
## ethnic_groupgroup E:test_prepnone 2.308 0.021547 *
## ethnic_groupgroup B:parent_marital_statusmarried 0.966 0.334542
## ethnic_groupgroup C:parent_marital_statusmarried 0.206 0.837140
## ethnic_groupgroup D:parent_marital_statusmarried -1.372 0.170989
## ethnic_groupgroup E:parent_marital_statusmarried -0.115 0.908733
## ethnic_groupgroup B:parent_marital_statussingle 1.976 0.048918 *
## ethnic_groupgroup C:parent_marital_statussingle 0.899 0.369157
## ethnic_groupgroup D:parent_marital_statussingle 0.374 0.708312
## ethnic_groupgroup E:parent_marital_statussingle 1.513 0.131102
## ethnic_groupgroup B:parent_marital_statuswidowed 0.481 0.630440
## ethnic_groupgroup C:parent_marital_statuswidowed 0.925 0.355741
## ethnic_groupgroup D:parent_marital_statuswidowed 0.054 0.956960
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 1.388 0.165839
## ethnic_groupgroup C:practice_sportregularly 1.402 0.161631
## ethnic_groupgroup D:practice_sportregularly 1.040 0.298794
## ethnic_groupgroup E:practice_sportregularly 1.453 0.147075
## ethnic_groupgroup B:practice_sportsometimes 1.281 0.200908
## ethnic_groupgroup C:practice_sportsometimes 2.067 0.039362 *
## ethnic_groupgroup D:practice_sportsometimes 1.101 0.271507
## ethnic_groupgroup E:practice_sportsometimes 1.348 0.178360
## ethnic_groupgroup B:is_first_childyes 1.203 0.229543
## ethnic_groupgroup C:is_first_childyes 0.172 0.863639
## ethnic_groupgroup D:is_first_childyes -0.104 0.917334
## ethnic_groupgroup E:is_first_childyes 0.001 0.999145
## ethnic_groupgroup B:transport_meansschool_bus -1.636 0.102593
## ethnic_groupgroup C:transport_meansschool_bus -2.256 0.024637 *
## ethnic_groupgroup D:transport_meansschool_bus -0.713 0.476094
## ethnic_groupgroup E:transport_meansschool_bus -1.845 0.065857 .
## ethnic_groupgroup B:wkly_study_hours> 10 -0.846 0.398354
## ethnic_groupgroup C:wkly_study_hours> 10 -0.070 0.944160
## ethnic_groupgroup D:wkly_study_hours> 10 0.027 0.978577
## ethnic_groupgroup E:wkly_study_hours> 10 -0.259 0.796117
## ethnic_groupgroup B:wkly_study_hours10-May -0.942 0.346753
## ethnic_groupgroup C:wkly_study_hours10-May -0.298 0.765813
## ethnic_groupgroup D:wkly_study_hours10-May -0.283 0.777517
## ethnic_groupgroup E:wkly_study_hours10-May -0.696 0.486909
## parent_educbachelor's degree:lunch_typestandard 0.107 0.914738
## parent_educhigh school:lunch_typestandard 0.197 0.843729
## parent_educmaster's degree:lunch_typestandard 0.896 0.370878
## parent_educsome college:lunch_typestandard 0.816 0.415002
## parent_educsome high school:lunch_typestandard 1.309 0.191356
## parent_educbachelor's degree:test_prepnone -0.628 0.530209
## parent_educhigh school:test_prepnone 0.522 0.601931
## parent_educmaster's degree:test_prepnone 0.065 0.948334
## parent_educsome college:test_prepnone -0.745 0.456580
## parent_educsome high school:test_prepnone 0.652 0.514864
## parent_educbachelor's degree:parent_marital_statusmarried -2.210 0.027665 *
## parent_educhigh school:parent_marital_statusmarried 0.688 0.491762
## parent_educmaster's degree:parent_marital_statusmarried 0.090 0.928128
## parent_educsome college:parent_marital_statusmarried -1.284 0.200068
## parent_educsome high school:parent_marital_statusmarried -0.756 0.449872
## parent_educbachelor's degree:parent_marital_statussingle -1.883 0.060511 .
## parent_educhigh school:parent_marital_statussingle 1.358 0.175196
## parent_educmaster's degree:parent_marital_statussingle 0.001 0.998882
## parent_educsome college:parent_marital_statussingle -0.899 0.369139
## parent_educsome high school:parent_marital_statussingle -0.164 0.869653
## parent_educbachelor's degree:parent_marital_statuswidowed -0.248 0.804406
## parent_educhigh school:parent_marital_statuswidowed -0.598 0.550415
## parent_educmaster's degree:parent_marital_statuswidowed -1.534 0.125904
## parent_educsome college:parent_marital_statuswidowed -0.949 0.343011
## parent_educsome high school:parent_marital_statuswidowed -0.490 0.624733
## parent_educbachelor's degree:practice_sportregularly -0.430 0.667700
## parent_educhigh school:practice_sportregularly -2.005 0.045673 *
## parent_educmaster's degree:practice_sportregularly 0.133 0.894397
## parent_educsome college:practice_sportregularly -0.051 0.959122
## parent_educsome high school:practice_sportregularly -0.550 0.582541
## parent_educbachelor's degree:practice_sportsometimes -1.539 0.124621
## parent_educhigh school:practice_sportsometimes -1.717 0.086818 .
## parent_educmaster's degree:practice_sportsometimes 0.756 0.450258
## parent_educsome college:practice_sportsometimes 0.145 0.884846
## parent_educsome high school:practice_sportsometimes 0.222 0.824708
## parent_educbachelor's degree:is_first_childyes 0.946 0.344850
## parent_educhigh school:is_first_childyes 1.512 0.131459
## parent_educmaster's degree:is_first_childyes 0.822 0.411676
## parent_educsome college:is_first_childyes 2.262 0.024229 *
## parent_educsome high school:is_first_childyes 1.128 0.260191
## parent_educbachelor's degree:transport_meansschool_bus 0.179 0.857717
## parent_educhigh school:transport_meansschool_bus 0.840 0.401533
## parent_educmaster's degree:transport_meansschool_bus 0.774 0.439287
## parent_educsome college:transport_meansschool_bus 0.889 0.374321
## parent_educsome high school:transport_meansschool_bus 1.443 0.149883
## parent_educbachelor's degree:wkly_study_hours> 10 -1.099 0.272654
## parent_educhigh school:wkly_study_hours> 10 -1.344 0.179724
## parent_educmaster's degree:wkly_study_hours> 10 -0.133 0.894038
## parent_educsome college:wkly_study_hours> 10 -0.960 0.337663
## parent_educsome high school:wkly_study_hours> 10 -1.060 0.289895
## parent_educbachelor's degree:wkly_study_hours10-May -0.376 0.707482
## parent_educhigh school:wkly_study_hours10-May -2.212 0.027535 *
## parent_educmaster's degree:wkly_study_hours10-May -0.163 0.870761
## parent_educsome college:wkly_study_hours10-May -0.593 0.553816
## parent_educsome high school:wkly_study_hours10-May -1.671 0.095514 .
## lunch_typestandard:test_prepnone -1.109 0.268237
## lunch_typestandard:parent_marital_statusmarried -1.990 0.047312 *
## lunch_typestandard:parent_marital_statussingle -0.806 0.420618
## lunch_typestandard:parent_marital_statuswidowed 0.119 0.905148
## lunch_typestandard:practice_sportregularly 1.335 0.182661
## lunch_typestandard:practice_sportsometimes 2.038 0.042245 *
## lunch_typestandard:is_first_childyes -1.204 0.229445
## lunch_typestandard:transport_meansschool_bus -1.310 0.191089
## lunch_typestandard:wkly_study_hours> 10 1.837 0.066989 .
## lunch_typestandard:wkly_study_hours10-May -0.192 0.848226
## test_prepnone:parent_marital_statusmarried 0.932 0.351667
## test_prepnone:parent_marital_statussingle -0.058 0.953813
## test_prepnone:parent_marital_statuswidowed -0.820 0.412702
## test_prepnone:practice_sportregularly 0.589 0.556054
## test_prepnone:practice_sportsometimes 0.935 0.350295
## test_prepnone:is_first_childyes 0.389 0.697562
## test_prepnone:transport_meansschool_bus 0.649 0.516419
## test_prepnone:wkly_study_hours> 10 -0.639 0.523517
## test_prepnone:wkly_study_hours10-May 0.452 0.651763
## parent_marital_statusmarried:practice_sportregularly 0.507 0.612191
## parent_marital_statussingle:practice_sportregularly -0.521 0.602548
## parent_marital_statuswidowed:practice_sportregularly -0.083 0.933822
## parent_marital_statusmarried:practice_sportsometimes 0.202 0.840388
## parent_marital_statussingle:practice_sportsometimes -0.522 0.601793
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -3.591 0.000373 ***
## parent_marital_statussingle:is_first_childyes -1.613 0.107478
## parent_marital_statuswidowed:is_first_childyes 0.744 0.457312
## parent_marital_statusmarried:transport_meansschool_bus 1.108 0.268571
## parent_marital_statussingle:transport_meansschool_bus -0.241 0.809421
## parent_marital_statuswidowed:transport_meansschool_bus -0.746 0.455903
## parent_marital_statusmarried:wkly_study_hours> 10 3.431 0.000666 ***
## parent_marital_statussingle:wkly_study_hours> 10 3.956 9.07e-05 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 0.804 0.421624
## parent_marital_statussingle:wkly_study_hours10-May 0.882 0.378225
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## practice_sportregularly:is_first_childyes -0.656 0.512067
## practice_sportsometimes:is_first_childyes -1.092 0.275662
## practice_sportregularly:transport_meansschool_bus 1.816 0.070179 .
## practice_sportsometimes:transport_meansschool_bus 1.180 0.238890
## practice_sportregularly:wkly_study_hours> 10 0.605 0.545817
## practice_sportsometimes:wkly_study_hours> 10 0.578 0.563797
## practice_sportregularly:wkly_study_hours10-May 1.459 0.145298
## practice_sportsometimes:wkly_study_hours10-May 0.071 0.943459
## is_first_childyes:transport_meansschool_bus -0.515 0.606629
## is_first_childyes:wkly_study_hours> 10 0.492 0.622891
## is_first_childyes:wkly_study_hours10-May -0.873 0.383295
## transport_meansschool_bus:wkly_study_hours> 10 0.164 0.870166
## transport_meansschool_bus:wkly_study_hours10-May 0.819 0.413185
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.87 on 383 degrees of freedom
## Multiple R-squared: 0.5303, Adjusted R-squared: 0.2777
## F-statistic: 2.099 on 206 and 383 DF, p-value: 2.19e-10stepwise_model_read <- step(full_fit_read, direction = "both", trace = 1)## Start: AIC=3174.13
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours)^2
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 614.8 64084 3163.8
## - parent_educ:wkly_study_hours 10 1420.6 64890 3167.2
## - parent_educ:transport_means 5 415.6 63885 3168.0
## - ethnic_group:parent_educ 20 3769.8 67239 3168.2
## - parent_educ:lunch_type 5 448.1 63918 3168.3
## - parent_educ:test_prep 5 452.4 63922 3168.3
## - gender:parent_marital_status 3 36.6 63506 3168.5
## - parent_marital_status:practice_sport 4 295.7 63765 3168.9
## - gender:parent_educ 5 629.0 64099 3170.0
## - transport_means:wkly_study_hours 2 123.0 63593 3171.3
## - gender:practice_sport 2 145.0 63615 3171.5
## - test_prep:practice_sport 2 164.3 63634 3171.7
## - ethnic_group:is_first_child 4 609.4 64079 3171.8
## - gender:wkly_study_hours 2 202.8 63672 3172.0
## - gender:test_prep 1 1.4 63471 3172.1
## - gender:transport_means 1 2.9 63473 3172.2
## - test_prep:is_first_child 1 25.1 63495 3172.4
## - gender:lunch_type 1 25.8 63495 3172.4
## - test_prep:wkly_study_hours 2 242.4 63712 3172.4
## - parent_educ:is_first_child 5 899.0 64369 3172.4
## - is_first_child:transport_means 1 44.0 63514 3172.5
## - practice_sport:is_first_child 2 259.9 63730 3172.5
## - test_prep:transport_means 1 69.9 63539 3172.8
## - is_first_child:wkly_study_hours 2 322.5 63792 3173.1
## - test_prep:parent_marital_status 2 337.8 63807 3173.3
## - parent_educ:parent_marital_status 13 2799.2 66269 3173.6
## - lunch_type:test_prep 1 203.7 63673 3174.0
## <none> 63470 3174.1
## - gender:is_first_child 1 230.7 63700 3174.3
## - lunch_type:is_first_child 1 240.1 63710 3174.4
## - parent_marital_status:transport_means 3 678.8 64148 3174.4
## - ethnic_group:practice_sport 8 1798.4 65268 3174.6
## - gender:ethnic_group 4 933.4 64403 3174.7
## - lunch_type:transport_means 1 284.2 63754 3174.8
## - ethnic_group:lunch_type 4 995.4 64465 3175.3
## - practice_sport:transport_means 2 595.4 64065 3175.6
## - ethnic_group:test_prep 4 1172.3 64642 3176.9
## - lunch_type:practice_sport 2 753.7 64223 3177.1
## - lunch_type:parent_marital_status 2 780.0 64250 3177.3
## - practice_sport:wkly_study_hours 4 1228.1 64698 3177.4
## - parent_educ:practice_sport 10 2564.7 66034 3177.5
## - lunch_type:wkly_study_hours 2 855.7 64325 3178.0
## - ethnic_group:transport_means 4 1492.9 64962 3179.9
## - ethnic_group:parent_marital_status 9 2935.6 66405 3182.8
## - parent_marital_status:wkly_study_hours 4 2936.1 66406 3192.8
## - parent_marital_status:is_first_child 2 2728.2 66198 3195.0
##
## Step: AIC=3163.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 3674.5 67759 3156.7
## - parent_educ:transport_means 5 373.1 64458 3157.2
## - parent_marital_status:practice_sport 4 207.2 64292 3157.7
## - parent_educ:test_prep 5 437.9 64522 3157.8
## - parent_educ:wkly_study_hours 10 1542.6 65627 3157.9
## - parent_educ:lunch_type 5 440.6 64525 3157.9
## - gender:parent_marital_status 3 40.5 64125 3158.2
## - gender:parent_educ 5 657.6 64742 3159.8
## - transport_means:wkly_study_hours 2 68.6 64153 3160.5
## - gender:wkly_study_hours 2 148.7 64233 3161.2
## - gender:practice_sport 2 163.3 64248 3161.3
## - ethnic_group:is_first_child 4 606.3 64691 3161.4
## - test_prep:practice_sport 2 177.1 64261 3161.4
## - gender:transport_means 1 1.5 64086 3161.8
## - parent_educ:parent_marital_status 13 2664.0 66748 3161.9
## - test_prep:is_first_child 1 10.1 64094 3161.9
## - gender:test_prep 1 11.1 64095 3161.9
## - gender:lunch_type 1 32.7 64117 3162.1
## - test_prep:wkly_study_hours 2 253.0 64337 3162.1
## - parent_educ:is_first_child 5 914.6 64999 3162.2
## - is_first_child:transport_means 1 51.4 64136 3162.3
## - practice_sport:is_first_child 2 272.2 64357 3162.3
## - test_prep:transport_means 1 62.9 64147 3162.4
## - test_prep:parent_marital_status 2 349.0 64433 3163.0
## - lunch_type:test_prep 1 162.2 64247 3163.3
## - is_first_child:wkly_study_hours 2 382.1 64467 3163.3
## - gender:is_first_child 1 171.5 64256 3163.4
## <none> 64084 3163.8
## - gender:ethnic_group 4 876.2 64961 3163.8
## - ethnic_group:practice_sport 8 1783.4 65868 3164.0
## - lunch_type:is_first_child 1 255.0 64339 3164.2
## - lunch_type:transport_means 1 257.3 64342 3164.2
## - parent_marital_status:transport_means 3 747.2 64832 3164.7
## - practice_sport:transport_means 2 575.9 64660 3165.1
## - ethnic_group:lunch_type 4 1030.9 65115 3165.2
## - parent_educ:practice_sport 10 2521.2 66606 3166.6
## - lunch_type:practice_sport 2 747.6 64832 3166.7
## - lunch_type:parent_marital_status 2 764.2 64849 3166.8
## - ethnic_group:test_prep 4 1220.5 65305 3167.0
## - practice_sport:wkly_study_hours 4 1277.6 65362 3167.5
## - lunch_type:wkly_study_hours 2 896.1 64981 3168.0
## - ethnic_group:transport_means 4 1568.2 65653 3170.1
## - ethnic_group:parent_marital_status 9 2898.4 66983 3171.9
## + ethnic_group:wkly_study_hours 8 614.8 63470 3174.1
## - parent_marital_status:wkly_study_hours 4 2786.9 66871 3180.9
## - parent_marital_status:is_first_child 2 2661.3 66746 3183.8
##
## Step: AIC=3156.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 1269.9 69029 3147.7
## - parent_educ:test_prep 5 307.0 68066 3149.4
## - parent_educ:lunch_type 5 386.5 68145 3150.1
## - parent_educ:transport_means 5 461.7 68221 3150.7
## - parent_marital_status:practice_sport 4 242.6 68001 3150.8
## - gender:parent_marital_status 3 138.7 67898 3151.9
## - ethnic_group:practice_sport 8 1348.4 69107 3152.3
## - gender:parent_educ 5 701.3 68460 3152.8
## - parent_educ:is_first_child 5 840.6 68600 3154.0
## - transport_means:wkly_study_hours 2 158.4 67917 3154.1
## - test_prep:practice_sport 2 181.0 67940 3154.3
## - gender:wkly_study_hours 2 187.1 67946 3154.3
## - is_first_child:wkly_study_hours 2 193.0 67952 3154.4
## - practice_sport:is_first_child 2 209.8 67969 3154.5
## - parent_educ:practice_sport 10 2091.0 69850 3154.6
## - test_prep:is_first_child 1 0.0 67759 3154.7
## - gender:lunch_type 1 1.5 67760 3154.7
## - gender:transport_means 1 6.0 67765 3154.8
## - gender:test_prep 1 28.8 67788 3155.0
## - is_first_child:transport_means 1 31.9 67791 3155.0
## - lunch_type:test_prep 1 39.0 67798 3155.1
## - gender:is_first_child 1 53.7 67813 3155.2
## - gender:practice_sport 2 289.5 68048 3155.2
## - parent_marital_status:transport_means 3 527.4 68286 3155.3
## - test_prep:wkly_study_hours 2 299.0 68058 3155.3
## - lunch_type:parent_marital_status 2 301.2 68060 3155.3
## - ethnic_group:is_first_child 4 776.5 68535 3155.4
## - test_prep:transport_means 1 93.8 67853 3155.5
## - test_prep:parent_marital_status 2 332.4 68091 3155.6
## - parent_educ:parent_marital_status 13 2982.5 70741 3156.1
## - gender:ethnic_group 4 905.4 68664 3156.5
## - practice_sport:transport_means 2 445.2 68204 3156.6
## <none> 67759 3156.7
## - lunch_type:is_first_child 1 315.4 68074 3157.5
## - lunch_type:transport_means 1 316.6 68076 3157.5
## - ethnic_group:test_prep 4 1135.3 68894 3158.5
## - ethnic_group:lunch_type 4 1174.9 68934 3158.9
## - practice_sport:wkly_study_hours 4 1254.5 69013 3159.5
## - lunch_type:practice_sport 2 898.1 68657 3160.5
## - ethnic_group:transport_means 4 1420.9 69180 3161.0
## - lunch_type:wkly_study_hours 2 1153.6 68912 3162.7
## + ethnic_group:parent_educ 20 3674.5 64084 3163.8
## - ethnic_group:parent_marital_status 9 2958.5 70717 3163.9
## - parent_marital_status:wkly_study_hours 4 2214.9 69974 3167.7
## + ethnic_group:wkly_study_hours 8 519.5 67239 3168.2
## - parent_marital_status:is_first_child 2 2405.1 70164 3173.3
##
## Step: AIC=3147.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 320.2 69349 3140.4
## - parent_educ:test_prep 5 383.5 69412 3140.9
## - parent_marital_status:practice_sport 4 281.9 69311 3142.1
## - parent_educ:transport_means 5 536.0 69565 3142.2
## - gender:parent_marital_status 3 108.9 69138 3142.6
## - ethnic_group:practice_sport 8 1371.2 70400 3143.3
## - gender:parent_educ 5 719.3 69748 3143.8
## - parent_educ:is_first_child 5 751.8 69781 3144.1
## - is_first_child:wkly_study_hours 2 140.8 69170 3144.9
## - transport_means:wkly_study_hours 2 190.3 69219 3145.3
## - practice_sport:is_first_child 2 196.8 69226 3145.4
## - test_prep:practice_sport 2 233.3 69262 3145.7
## - test_prep:is_first_child 1 0.2 69029 3145.7
## - gender:transport_means 1 0.3 69029 3145.7
## - gender:lunch_type 1 3.0 69032 3145.7
## - gender:practice_sport 2 243.8 69273 3145.8
## - lunch_type:test_prep 1 17.2 69046 3145.8
## - gender:test_prep 1 29.3 69058 3145.9
## - is_first_child:transport_means 1 45.0 69074 3146.1
## - gender:is_first_child 1 76.7 69106 3146.3
## - gender:wkly_study_hours 2 313.2 69342 3146.3
## - parent_marital_status:transport_means 3 553.7 69582 3146.4
## - test_prep:parent_marital_status 2 325.4 69354 3146.4
## - test_prep:transport_means 1 96.8 69126 3146.5
## - lunch_type:parent_marital_status 2 332.8 69362 3146.5
## - practice_sport:transport_means 2 339.7 69369 3146.6
## - ethnic_group:is_first_child 4 835.0 69864 3146.8
## - test_prep:wkly_study_hours 2 400.0 69429 3147.1
## - gender:ethnic_group 4 886.0 69915 3147.2
## - parent_educ:practice_sport 10 2344.8 71374 3147.4
## <none> 69029 3147.7
## - lunch_type:is_first_child 1 244.1 69273 3147.8
## - ethnic_group:lunch_type 4 956.4 69985 3147.8
## - practice_sport:wkly_study_hours 4 1068.0 70097 3148.7
## - lunch_type:transport_means 1 366.9 69396 3148.8
## - parent_educ:parent_marital_status 13 3281.5 72310 3149.1
## - ethnic_group:test_prep 4 1108.8 70138 3149.1
## - lunch_type:practice_sport 2 846.3 69875 3150.9
## - ethnic_group:transport_means 4 1324.6 70353 3150.9
## - lunch_type:wkly_study_hours 2 1037.5 70066 3152.5
## - ethnic_group:parent_marital_status 9 3215.7 72244 3156.5
## + parent_educ:wkly_study_hours 10 1269.9 67759 3156.7
## + ethnic_group:parent_educ 20 3401.8 65627 3157.9
## + ethnic_group:wkly_study_hours 8 590.3 68439 3158.6
## - parent_marital_status:wkly_study_hours 4 2375.7 71404 3159.6
## - parent_marital_status:is_first_child 2 2553.3 71582 3165.1
##
## Step: AIC=3140.4
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 341.0 69690 3133.3
## - parent_marital_status:practice_sport 4 306.4 69655 3135.0
## - parent_educ:transport_means 5 558.5 69908 3135.1
## - ethnic_group:practice_sport 8 1291.4 70640 3135.3
## - gender:parent_marital_status 3 130.7 69480 3135.5
## - gender:parent_educ 5 692.2 70041 3136.3
## - parent_educ:is_first_child 5 738.5 70088 3136.7
## - is_first_child:wkly_study_hours 2 148.9 69498 3137.7
## - practice_sport:is_first_child 2 212.5 69561 3138.2
## - transport_means:wkly_study_hours 2 223.6 69573 3138.3
## - gender:transport_means 1 0.1 69349 3138.4
## - test_prep:is_first_child 1 1.4 69350 3138.4
## - gender:practice_sport 2 240.3 69589 3138.4
## - gender:lunch_type 1 11.3 69360 3138.5
## - lunch_type:test_prep 1 17.1 69366 3138.6
## - test_prep:practice_sport 2 258.3 69607 3138.6
## - gender:test_prep 1 32.6 69382 3138.7
## - is_first_child:transport_means 1 42.2 69391 3138.8
## - gender:wkly_study_hours 2 292.4 69641 3138.9
## - lunch_type:parent_marital_status 2 322.6 69672 3139.1
## - test_prep:parent_marital_status 2 339.4 69688 3139.3
## - test_prep:transport_means 1 110.2 69459 3139.3
## - gender:is_first_child 1 123.4 69472 3139.4
## - parent_marital_status:transport_means 3 609.9 69959 3139.6
## - ethnic_group:is_first_child 4 848.6 70198 3139.6
## - gender:ethnic_group 4 857.9 70207 3139.7
## - test_prep:wkly_study_hours 2 403.6 69753 3139.8
## - practice_sport:transport_means 2 407.8 69757 3139.9
## - lunch_type:is_first_child 1 218.0 69567 3140.3
## <none> 69349 3140.4
## - ethnic_group:lunch_type 4 951.4 70300 3140.4
## - parent_educ:practice_sport 10 2413.6 71763 3140.6
## - lunch_type:transport_means 1 377.6 69727 3141.6
## - practice_sport:wkly_study_hours 4 1124.5 70474 3141.9
## - ethnic_group:test_prep 4 1131.5 70481 3141.9
## - parent_educ:parent_marital_status 13 3369.7 72719 3142.4
## - lunch_type:practice_sport 2 809.1 70158 3143.2
## - ethnic_group:transport_means 4 1299.6 70649 3143.4
## - lunch_type:wkly_study_hours 2 993.1 70342 3144.8
## + parent_educ:lunch_type 5 320.2 69029 3147.7
## - ethnic_group:parent_marital_status 9 3147.4 72496 3148.6
## + parent_educ:wkly_study_hours 10 1203.6 68145 3150.1
## + ethnic_group:parent_educ 20 3421.3 65928 3150.6
## + ethnic_group:wkly_study_hours 8 565.0 68784 3151.6
## - parent_marital_status:wkly_study_hours 4 2520.8 71870 3153.5
## - parent_marital_status:is_first_child 2 2752.7 72102 3159.4
##
## Step: AIC=3133.3
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 317.6 70008 3128.0
## - ethnic_group:practice_sport 8 1274.2 70964 3128.0
## - gender:parent_marital_status 3 123.8 69814 3128.3
## - gender:parent_educ 5 652.4 70342 3128.8
## - parent_educ:transport_means 5 667.2 70357 3128.9
## - parent_educ:is_first_child 5 796.7 70487 3130.0
## - is_first_child:wkly_study_hours 2 124.6 69815 3130.3
## - practice_sport:is_first_child 2 200.9 69891 3131.0
## - transport_means:wkly_study_hours 2 208.5 69899 3131.1
## - gender:practice_sport 2 223.7 69914 3131.2
## - test_prep:practice_sport 2 229.3 69919 3131.2
## - test_prep:is_first_child 1 0.3 69690 3131.3
## - gender:transport_means 1 1.0 69691 3131.3
## - gender:lunch_type 1 8.7 69699 3131.4
## - lunch_type:test_prep 1 19.1 69709 3131.5
## - lunch_type:parent_marital_status 2 264.9 69955 3131.5
## - gender:ethnic_group 4 753.5 70444 3131.6
## - gender:test_prep 1 55.9 69746 3131.8
## - test_prep:parent_marital_status 2 301.2 69991 3131.8
## - is_first_child:transport_means 1 67.9 69758 3131.9
## - gender:wkly_study_hours 2 310.5 70001 3131.9
## - test_prep:transport_means 1 100.3 69790 3132.2
## - gender:is_first_child 1 104.9 69795 3132.2
## - parent_marital_status:transport_means 3 587.6 70278 3132.2
## - ethnic_group:is_first_child 4 907.0 70597 3132.9
## - practice_sport:transport_means 2 436.3 70126 3133.0
## - test_prep:wkly_study_hours 2 443.2 70133 3133.0
## <none> 69690 3133.3
## - ethnic_group:test_prep 4 951.6 70642 3133.3
## - lunch_type:is_first_child 1 248.8 69939 3133.4
## - parent_educ:practice_sport 10 2425.2 72115 3133.5
## - ethnic_group:lunch_type 4 1002.5 70692 3133.7
## - lunch_type:transport_means 1 375.0 70065 3134.5
## - parent_educ:parent_marital_status 13 3343.7 73034 3134.9
## - practice_sport:wkly_study_hours 4 1153.2 70843 3135.0
## - ethnic_group:transport_means 4 1310.7 71001 3136.3
## - lunch_type:practice_sport 2 917.5 70608 3137.0
## - lunch_type:wkly_study_hours 2 1061.6 70752 3138.2
## + parent_educ:test_prep 5 341.0 69349 3140.4
## - ethnic_group:parent_marital_status 9 3065.0 72755 3140.7
## + parent_educ:lunch_type 5 277.8 69412 3140.9
## + parent_educ:wkly_study_hours 10 1255.7 68434 3142.6
## + ethnic_group:wkly_study_hours 8 565.8 69124 3144.5
## + ethnic_group:parent_educ 20 3212.4 66478 3145.4
## - parent_marital_status:wkly_study_hours 4 2684.2 72374 3147.6
## - parent_marital_status:is_first_child 2 2781.2 72471 3152.4
##
## Step: AIC=3127.98
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 122.7 70130 3123.0
## - ethnic_group:practice_sport 8 1365.0 71373 3123.4
## - gender:parent_educ 5 663.1 70671 3123.5
## - parent_educ:transport_means 5 690.2 70698 3123.8
## - lunch_type:parent_marital_status 3 322.0 70330 3124.7
## - parent_educ:is_first_child 5 800.9 70809 3124.7
## - practice_sport:is_first_child 2 150.9 70159 3125.2
## - is_first_child:wkly_study_hours 2 163.9 70172 3125.4
## - transport_means:wkly_study_hours 2 204.8 70212 3125.7
## - test_prep:practice_sport 2 236.5 70244 3126.0
## - gender:ethnic_group 4 714.8 70722 3126.0
## - test_prep:is_first_child 1 0.6 70008 3126.0
## - gender:transport_means 1 1.9 70010 3126.0
## - gender:lunch_type 1 7.2 70015 3126.0
## - lunch_type:test_prep 1 18.2 70026 3126.1
## - gender:practice_sport 2 264.3 70272 3126.2
## - test_prep:parent_marital_status 2 280.5 70288 3126.3
## - gender:test_prep 1 66.7 70074 3126.5
## - is_first_child:transport_means 1 87.2 70095 3126.7
## - test_prep:transport_means 1 93.7 70101 3126.8
## - gender:is_first_child 1 97.3 70105 3126.8
## - gender:wkly_study_hours 2 342.9 70351 3126.9
## - parent_marital_status:transport_means 3 583.7 70591 3126.9
## - practice_sport:transport_means 2 401.2 70409 3127.3
## - lunch_type:is_first_child 1 177.5 70185 3127.5
## - ethnic_group:is_first_child 4 929.5 70937 3127.8
## - ethnic_group:test_prep 4 940.7 70948 3127.9
## - test_prep:wkly_study_hours 2 463.2 70471 3127.9
## <none> 70008 3128.0
## - parent_educ:practice_sport 10 2449.6 72457 3128.3
## - lunch_type:transport_means 1 337.8 70345 3128.8
## - parent_educ:parent_marital_status 14 3565.4 73573 3129.3
## - ethnic_group:lunch_type 4 1115.6 71123 3129.3
## - practice_sport:wkly_study_hours 4 1150.0 71158 3129.6
## - ethnic_group:transport_means 4 1283.9 71292 3130.7
## - lunch_type:practice_sport 2 877.2 70885 3131.3
## - lunch_type:wkly_study_hours 2 1099.1 71107 3133.2
## + parent_marital_status:practice_sport 4 317.6 69690 3133.3
## - ethnic_group:parent_marital_status 10 3190.9 73199 3134.3
## + parent_educ:test_prep 5 352.3 69655 3135.0
## + parent_educ:lunch_type 5 297.6 69710 3135.5
## + parent_educ:wkly_study_hours 10 1290.0 68718 3137.0
## + ethnic_group:wkly_study_hours 8 481.0 69527 3139.9
## + ethnic_group:parent_educ 20 3249.9 66758 3139.9
## - parent_marital_status:wkly_study_hours 5 2853.2 72861 3141.6
## - parent_marital_status:is_first_child 2 3039.8 73048 3149.1
##
## Step: AIC=3123.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 1356.7 71487 3118.3
## - gender:parent_educ 5 677.1 70808 3118.7
## - parent_educ:transport_means 5 685.0 70815 3118.8
## - parent_educ:is_first_child 5 819.9 70950 3119.9
## - lunch_type:parent_marital_status 3 369.0 70499 3120.1
## - practice_sport:is_first_child 2 144.7 70275 3120.2
## - is_first_child:wkly_study_hours 2 152.6 70283 3120.3
## - transport_means:wkly_study_hours 2 204.9 70335 3120.7
## - gender:ethnic_group 4 700.0 70830 3120.9
## - test_prep:is_first_child 1 0.5 70131 3121.0
## - gender:transport_means 1 1.0 70131 3121.0
## - gender:lunch_type 1 4.8 70135 3121.1
## - lunch_type:test_prep 1 21.6 70152 3121.2
## - test_prep:practice_sport 2 266.1 70396 3121.2
## - gender:practice_sport 2 277.7 70408 3121.3
## - test_prep:parent_marital_status 2 280.8 70411 3121.4
## - gender:test_prep 1 80.0 70210 3121.7
## - test_prep:transport_means 1 91.3 70222 3121.8
## - is_first_child:transport_means 1 113.9 70244 3122.0
## - gender:is_first_child 1 114.3 70245 3122.0
## - gender:wkly_study_hours 2 363.0 70493 3122.1
## - practice_sport:transport_means 2 389.5 70520 3122.3
## - parent_marital_status:transport_means 3 660.2 70791 3122.5
## - lunch_type:is_first_child 1 183.4 70314 3122.6
## - ethnic_group:is_first_child 4 913.5 71044 3122.7
## - test_prep:wkly_study_hours 2 455.4 70586 3122.8
## - ethnic_group:test_prep 4 952.9 71083 3123.0
## <none> 70130 3123.0
## - parent_educ:parent_marital_status 14 3455.4 73586 3123.4
## - lunch_type:transport_means 1 356.3 70487 3124.0
## - ethnic_group:lunch_type 4 1108.7 71239 3124.3
## - parent_educ:practice_sport 10 2585.2 72716 3124.4
## - practice_sport:wkly_study_hours 4 1194.7 71325 3125.0
## - ethnic_group:transport_means 4 1264.1 71395 3125.6
## - lunch_type:practice_sport 2 959.8 71090 3127.0
## + gender:parent_marital_status 3 122.7 70008 3128.0
## - lunch_type:wkly_study_hours 2 1110.6 71241 3128.3
## + parent_marital_status:practice_sport 4 316.5 69814 3128.3
## - ethnic_group:parent_marital_status 10 3250.3 73381 3129.7
## + parent_educ:test_prep 5 345.4 69785 3130.1
## + parent_educ:lunch_type 5 315.8 69815 3130.3
## + parent_educ:wkly_study_hours 10 1252.2 68878 3132.4
## + ethnic_group:parent_educ 20 3339.0 66791 3134.2
## + ethnic_group:wkly_study_hours 8 511.2 69619 3134.7
## - parent_marital_status:wkly_study_hours 5 2844.3 72975 3136.5
## - parent_marital_status:is_first_child 2 3138.1 73269 3144.8
##
## Step: AIC=3118.32
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 548.5 72036 3112.8
## - gender:parent_educ 5 581.6 72069 3113.1
## - gender:ethnic_group 4 534.8 72022 3114.7
## - practice_sport:is_first_child 2 121.8 71609 3115.3
## - lunch_type:parent_marital_status 3 394.4 71882 3115.6
## - is_first_child:wkly_study_hours 2 177.5 71665 3115.8
## - test_prep:practice_sport 2 196.3 71683 3115.9
## - parent_educ:is_first_child 5 939.4 72427 3116.0
## - transport_means:wkly_study_hours 2 221.2 71708 3116.1
## - lunch_type:test_prep 1 0.0 71487 3116.3
## - gender:lunch_type 1 0.1 71487 3116.3
## - gender:transport_means 1 0.3 71487 3116.3
## - test_prep:is_first_child 1 0.7 71488 3116.3
## - gender:test_prep 1 50.9 71538 3116.7
## - gender:is_first_child 1 53.6 71541 3116.8
## - test_prep:parent_marital_status 2 313.1 71800 3116.9
## - ethnic_group:is_first_child 4 825.4 72313 3117.1
## - test_prep:wkly_study_hours 2 338.3 71825 3117.1
## - test_prep:transport_means 1 106.9 71594 3117.2
## - practice_sport:transport_means 2 376.1 71863 3117.4
## - is_first_child:transport_means 1 164.3 71651 3117.7
## - ethnic_group:test_prep 4 919.2 72406 3117.9
## - gender:practice_sport 2 453.1 71940 3118.1
## <none> 71487 3118.3
## - gender:wkly_study_hours 2 487.4 71974 3118.3
## - lunch_type:is_first_child 1 245.8 71733 3118.3
## - lunch_type:transport_means 1 258.5 71746 3118.4
## - parent_educ:parent_marital_status 14 3522.4 75010 3118.7
## - parent_marital_status:transport_means 3 781.1 72268 3118.7
## - parent_educ:practice_sport 10 2650.7 74138 3119.8
## - practice_sport:wkly_study_hours 4 1180.8 72668 3120.0
## - ethnic_group:lunch_type 4 1274.7 72762 3120.8
## - ethnic_group:transport_means 4 1324.6 72812 3121.2
## - lunch_type:practice_sport 2 969.1 72456 3122.3
## + parent_marital_status:practice_sport 4 402.2 71085 3123.0
## + ethnic_group:practice_sport 8 1356.7 70130 3123.0
## - lunch_type:wkly_study_hours 2 1089.7 72577 3123.2
## + gender:parent_marital_status 3 114.4 71373 3123.4
## - ethnic_group:parent_marital_status 10 3370.4 74858 3125.5
## + parent_educ:test_prep 5 312.5 71175 3125.7
## + parent_educ:lunch_type 5 224.8 71262 3126.5
## + parent_educ:wkly_study_hours 10 1304.6 70182 3127.4
## + ethnic_group:wkly_study_hours 8 473.3 71014 3130.4
## - parent_marital_status:wkly_study_hours 5 2938.9 74426 3132.1
## + ethnic_group:parent_educ 20 2867.8 68619 3134.2
## - parent_marital_status:is_first_child 2 2933.5 74421 3138.1
##
## Step: AIC=3112.83
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 603.8 72639 3107.8
## - gender:ethnic_group 4 475.9 72512 3108.7
## - practice_sport:is_first_child 2 88.0 72124 3109.6
## - is_first_child:wkly_study_hours 2 178.3 72214 3110.3
## - test_prep:practice_sport 2 197.3 72233 3110.4
## - lunch_type:parent_marital_status 3 454.7 72490 3110.5
## - parent_educ:is_first_child 5 958.0 72994 3110.6
## - transport_means:wkly_study_hours 2 234.3 72270 3110.7
## - gender:transport_means 1 0.0 72036 3110.8
## - test_prep:is_first_child 1 0.9 72036 3110.8
## - gender:lunch_type 1 1.7 72037 3110.8
## - lunch_type:test_prep 1 2.7 72038 3110.8
## - gender:test_prep 1 37.7 72073 3111.1
## - test_prep:parent_marital_status 2 287.2 72323 3111.2
## - gender:is_first_child 1 49.1 72085 3111.2
## - practice_sport:transport_means 2 304.8 72340 3111.3
## - test_prep:wkly_study_hours 2 352.0 72388 3111.7
## - is_first_child:transport_means 1 135.0 72171 3111.9
## - ethnic_group:is_first_child 4 874.0 72910 3111.9
## - test_prep:transport_means 1 146.1 72182 3112.0
## - parent_marital_status:transport_means 3 668.1 72704 3112.3
## - gender:wkly_study_hours 2 433.5 72469 3112.4
## - parent_educ:parent_marital_status 14 3444.3 75480 3112.4
## - ethnic_group:test_prep 4 945.8 72981 3112.5
## - gender:practice_sport 2 458.7 72494 3112.6
## - lunch_type:is_first_child 1 235.4 72271 3112.8
## <none> 72036 3112.8
## - lunch_type:transport_means 1 251.0 72287 3112.9
## - parent_educ:practice_sport 10 2633.4 74669 3114.0
## - practice_sport:wkly_study_hours 4 1297.2 73333 3115.4
## - ethnic_group:lunch_type 4 1387.9 73424 3116.1
## - ethnic_group:transport_means 4 1456.2 73492 3116.6
## - lunch_type:practice_sport 2 986.4 73022 3116.8
## + parent_marital_status:practice_sport 4 414.6 71621 3117.4
## + gender:parent_marital_status 3 109.2 71926 3117.9
## + parent_educ:transport_means 5 548.5 71487 3118.3
## - lunch_type:wkly_study_hours 2 1169.8 73205 3118.3
## + ethnic_group:practice_sport 8 1220.2 70815 3118.8
## + parent_educ:test_prep 5 395.4 71640 3119.6
## - ethnic_group:parent_marital_status 10 3435.4 75471 3120.3
## + parent_educ:lunch_type 5 241.7 71794 3120.8
## + parent_educ:wkly_study_hours 10 1335.5 70700 3121.8
## + ethnic_group:wkly_study_hours 8 495.2 71540 3124.8
## - parent_marital_status:wkly_study_hours 5 3004.4 75040 3126.9
## + ethnic_group:parent_educ 20 3017.4 69018 3127.6
## - parent_marital_status:is_first_child 2 2981.2 75017 3132.8
##
## Step: AIC=3107.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:ethnic_group +
## gender:lunch_type + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 357.5 72997 3102.7
## - parent_educ:is_first_child 5 838.9 73478 3104.5
## - practice_sport:is_first_child 2 105.8 72745 3104.6
## - lunch_type:parent_marital_status 3 422.0 73061 3105.2
## - is_first_child:wkly_study_hours 2 205.4 72845 3105.4
## - transport_means:wkly_study_hours 2 231.0 72870 3105.6
## - gender:transport_means 1 0.0 72639 3105.8
## - gender:lunch_type 1 1.4 72641 3105.8
## - test_prep:is_first_child 1 4.8 72644 3105.8
## - lunch_type:test_prep 1 11.0 72650 3105.8
## - test_prep:practice_sport 2 260.4 72900 3105.9
## - test_prep:parent_marital_status 2 267.3 72907 3105.9
## - gender:test_prep 1 27.3 72667 3106.0
## - practice_sport:transport_means 2 287.5 72927 3106.1
## - gender:is_first_child 1 46.8 72686 3106.1
## - ethnic_group:test_prep 4 856.3 73496 3106.7
## - ethnic_group:is_first_child 4 858.1 73497 3106.7
## - is_first_child:transport_means 1 127.0 72766 3106.8
## - test_prep:transport_means 1 128.8 72768 3106.8
## - test_prep:wkly_study_hours 2 412.9 73052 3107.1
## - gender:wkly_study_hours 2 454.8 73094 3107.4
## - gender:practice_sport 2 463.1 73103 3107.5
## - lunch_type:is_first_child 1 216.9 72856 3107.5
## - parent_marital_status:transport_means 3 724.1 73363 3107.6
## <none> 72639 3107.8
## - parent_educ:practice_sport 10 2551.6 75191 3108.1
## - lunch_type:transport_means 1 333.5 72973 3108.5
## - parent_educ:parent_marital_status 14 3774.3 76414 3109.6
## - practice_sport:wkly_study_hours 4 1233.1 73872 3109.7
## - ethnic_group:lunch_type 4 1289.5 73929 3110.1
## - lunch_type:practice_sport 2 942.3 73582 3111.4
## + parent_marital_status:practice_sport 4 431.9 72207 3112.2
## - ethnic_group:transport_means 4 1600.7 74240 3112.6
## + gender:parent_educ 5 603.8 72036 3112.8
## + gender:parent_marital_status 3 108.8 72531 3112.9
## - lunch_type:wkly_study_hours 2 1157.9 73797 3113.1
## + parent_educ:transport_means 5 570.6 72069 3113.1
## - ethnic_group:parent_marital_status 10 3305.3 75945 3114.0
## + ethnic_group:practice_sport 8 1130.0 71509 3114.5
## + parent_educ:test_prep 5 351.2 72288 3114.9
## + parent_educ:lunch_type 5 235.7 72404 3115.8
## + parent_educ:wkly_study_hours 10 1314.3 71325 3117.0
## + ethnic_group:wkly_study_hours 8 515.2 72124 3119.6
## + ethnic_group:parent_educ 20 3119.5 69520 3121.9
## - parent_marital_status:wkly_study_hours 5 3076.4 75716 3122.2
## - parent_marital_status:is_first_child 2 2985.7 75625 3127.5
##
## Step: AIC=3102.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 121.5 73118 3099.6
## - lunch_type:parent_marital_status 3 402.0 73399 3099.9
## - is_first_child:wkly_study_hours 2 204.6 73201 3100.3
## - parent_educ:is_first_child 5 960.2 73957 3100.4
## - ethnic_group:test_prep 4 712.7 73710 3100.4
## - transport_means:wkly_study_hours 2 234.6 73231 3100.5
## - gender:lunch_type 1 0.3 72997 3100.7
## - gender:transport_means 1 1.6 72998 3100.7
## - test_prep:parent_marital_status 2 250.2 73247 3100.7
## - test_prep:is_first_child 1 5.9 73003 3100.7
## - test_prep:practice_sport 2 258.1 73255 3100.7
## - lunch_type:test_prep 1 18.8 73016 3100.8
## - gender:test_prep 1 19.3 73016 3100.8
## - practice_sport:transport_means 2 282.8 73280 3100.9
## - gender:is_first_child 1 55.7 73052 3101.1
## - ethnic_group:is_first_child 4 838.1 73835 3101.4
## - test_prep:transport_means 1 135.7 73132 3101.7
## - is_first_child:transport_means 1 147.7 73145 3101.8
## - test_prep:wkly_study_hours 2 417.8 73415 3102.0
## - gender:practice_sport 2 467.7 73465 3102.4
## - lunch_type:is_first_child 1 223.6 73220 3102.4
## <none> 72997 3102.7
## - gender:wkly_study_hours 2 497.9 73495 3102.7
## - parent_marital_status:transport_means 3 785.6 73782 3103.0
## - parent_educ:practice_sport 10 2563.4 75560 3103.0
## - lunch_type:transport_means 1 326.1 73323 3103.3
## - ethnic_group:lunch_type 4 1273.0 74270 3104.8
## - practice_sport:wkly_study_hours 4 1285.8 74283 3104.9
## - parent_educ:parent_marital_status 14 3916.8 76914 3105.5
## - lunch_type:practice_sport 2 1063.9 74061 3107.2
## + parent_marital_status:practice_sport 4 401.1 72596 3107.4
## - ethnic_group:transport_means 4 1601.0 74598 3107.4
## - ethnic_group:parent_marital_status 10 3170.2 76167 3107.7
## + gender:ethnic_group 4 357.5 72639 3107.8
## + gender:parent_marital_status 3 100.5 72896 3107.8
## - lunch_type:wkly_study_hours 2 1180.5 74177 3108.1
## + parent_educ:transport_means 5 515.8 72481 3108.5
## + gender:parent_educ 5 485.3 72512 3108.7
## + ethnic_group:practice_sport 8 1051.0 71946 3110.1
## + parent_educ:test_prep 5 256.9 72740 3110.6
## + parent_educ:lunch_type 5 226.0 72771 3110.8
## + parent_educ:wkly_study_hours 10 1282.6 71714 3112.2
## + ethnic_group:wkly_study_hours 8 491.4 72505 3114.7
## - parent_marital_status:wkly_study_hours 5 3086.2 76083 3117.1
## + ethnic_group:parent_educ 20 3022.3 69974 3117.7
## - parent_marital_status:is_first_child 2 3076.4 76073 3123.0
##
## Step: AIC=3099.63
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 3 374.8 73493 3096.7
## - is_first_child:wkly_study_hours 2 186.9 73305 3097.1
## - parent_educ:is_first_child 5 949.9 74068 3097.2
## - ethnic_group:test_prep 4 732.4 73851 3097.5
## - transport_means:wkly_study_hours 2 238.0 73356 3097.6
## - test_prep:parent_marital_status 2 246.9 73365 3097.6
## - gender:lunch_type 1 0.3 73119 3097.6
## - test_prep:is_first_child 1 1.5 73120 3097.6
## - gender:transport_means 1 2.9 73121 3097.7
## - lunch_type:test_prep 1 23.0 73141 3097.8
## - practice_sport:transport_means 2 271.5 73390 3097.8
## - gender:test_prep 1 24.4 73143 3097.8
## - test_prep:practice_sport 2 282.1 73400 3097.9
## - gender:is_first_child 1 66.2 73184 3098.2
## - ethnic_group:is_first_child 4 870.1 73988 3098.6
## - test_prep:transport_means 1 138.4 73257 3098.8
## - test_prep:wkly_study_hours 2 402.6 73521 3098.9
## - is_first_child:transport_means 1 164.6 73283 3099.0
## - gender:practice_sport 2 455.9 73574 3099.3
## - gender:wkly_study_hours 2 489.8 73608 3099.6
## - lunch_type:is_first_child 1 245.7 73364 3099.6
## - parent_marital_status:transport_means 3 746.7 73865 3099.6
## <none> 73118 3099.6
## - parent_educ:practice_sport 10 2528.0 75646 3099.7
## - lunch_type:transport_means 1 326.5 73445 3100.3
## - ethnic_group:lunch_type 4 1294.0 74412 3102.0
## - parent_educ:parent_marital_status 14 3861.6 76980 3102.0
## - practice_sport:wkly_study_hours 4 1302.5 74421 3102.1
## + practice_sport:is_first_child 2 121.5 72997 3102.7
## - ethnic_group:transport_means 4 1550.5 74669 3104.0
## - lunch_type:practice_sport 2 1065.3 74184 3104.2
## - ethnic_group:parent_marital_status 10 3109.3 76228 3104.2
## + gender:ethnic_group 4 373.1 72745 3104.6
## + parent_marital_status:practice_sport 4 367.7 72751 3104.7
## + gender:parent_marital_status 3 88.8 73030 3104.9
## - lunch_type:wkly_study_hours 2 1188.6 74307 3105.1
## + gender:parent_educ 5 501.0 72617 3105.6
## + parent_educ:transport_means 5 474.9 72643 3105.8
## + ethnic_group:practice_sport 8 1036.1 72082 3107.2
## + parent_educ:test_prep 5 245.0 72873 3107.7
## + parent_educ:lunch_type 5 228.7 72890 3107.8
## + parent_educ:wkly_study_hours 10 1277.4 71841 3109.2
## + ethnic_group:wkly_study_hours 8 505.9 72612 3111.5
## - parent_marital_status:wkly_study_hours 5 3089.3 76208 3114.1
## + ethnic_group:parent_educ 20 2920.9 70197 3115.6
## - parent_marital_status:is_first_child 2 3028.3 76147 3119.6
##
## Step: AIC=3096.65
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:is_first_child 5 908.9 74402 3093.9
## - is_first_child:wkly_study_hours 2 173.4 73667 3094.0
## - test_prep:parent_marital_status 2 234.7 73728 3094.5
## - test_prep:is_first_child 1 1.1 73494 3094.7
## - ethnic_group:test_prep 4 753.5 74247 3094.7
## - gender:lunch_type 1 6.4 73500 3094.7
## - gender:transport_means 1 6.7 73500 3094.7
## - lunch_type:test_prep 1 20.6 73514 3094.8
## - practice_sport:transport_means 2 273.6 73767 3094.8
## - transport_means:wkly_study_hours 2 274.4 73767 3094.8
## - gender:test_prep 1 35.5 73529 3094.9
## - test_prep:practice_sport 2 290.9 73784 3095.0
## - ethnic_group:is_first_child 4 829.3 74322 3095.3
## - gender:is_first_child 1 81.0 73574 3095.3
## - test_prep:transport_means 1 136.1 73629 3095.7
## - test_prep:wkly_study_hours 2 402.3 73895 3095.9
## - gender:practice_sport 2 412.2 73905 3095.9
## - is_first_child:transport_means 1 175.2 73668 3096.1
## - gender:wkly_study_hours 2 431.3 73924 3096.1
## - lunch_type:is_first_child 1 218.5 73712 3096.4
## - parent_marital_status:transport_means 3 743.8 74237 3096.6
## <none> 73493 3096.7
## - parent_educ:practice_sport 10 2548.8 76042 3096.8
## - lunch_type:transport_means 1 328.3 73821 3097.3
## - practice_sport:wkly_study_hours 4 1295.6 74789 3099.0
## - parent_educ:parent_marital_status 14 3920.7 77414 3099.3
## + lunch_type:parent_marital_status 3 374.8 73118 3099.6
## - ethnic_group:lunch_type 4 1393.2 74886 3099.7
## + practice_sport:is_first_child 2 94.3 73399 3099.9
## - lunch_type:practice_sport 2 998.0 74491 3100.6
## - ethnic_group:parent_marital_status 10 3049.2 76542 3100.6
## - ethnic_group:transport_means 4 1542.9 75036 3100.9
## - lunch_type:wkly_study_hours 2 1093.4 74587 3101.4
## + gender:parent_marital_status 3 124.4 73369 3101.7
## + gender:ethnic_group 4 351.9 73141 3101.8
## + parent_educ:transport_means 5 521.3 72972 3102.4
## + gender:parent_educ 5 479.0 73014 3102.8
## + parent_marital_status:practice_sport 5 428.2 73065 3103.2
## + ethnic_group:practice_sport 8 1039.1 72454 3104.2
## + parent_educ:lunch_type 5 221.6 73272 3104.9
## + parent_educ:test_prep 5 214.7 73278 3104.9
## + parent_educ:wkly_study_hours 10 1282.2 72211 3106.3
## + ethnic_group:wkly_study_hours 8 478.5 73015 3108.8
## - parent_marital_status:wkly_study_hours 5 2984.5 76478 3110.1
## + ethnic_group:parent_educ 20 2625.3 70868 3115.2
## - parent_marital_status:is_first_child 2 3010.8 76504 3116.3
##
## Step: AIC=3093.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## is_first_child:wkly_study_hours + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 116.1 74518 3090.8
## - test_prep:parent_marital_status 2 216.2 74618 3091.6
## - test_prep:is_first_child 1 1.0 74403 3091.9
## - gender:transport_means 1 2.7 74405 3091.9
## - gender:lunch_type 1 4.7 74407 3091.9
## - transport_means:wkly_study_hours 2 263.8 74666 3092.0
## - ethnic_group:test_prep 4 772.1 75174 3092.0
## - lunch_type:test_prep 1 14.6 74417 3092.0
## - practice_sport:transport_means 2 278.7 74681 3092.1
## - gender:test_prep 1 36.6 74439 3092.2
## - ethnic_group:is_first_child 4 820.4 75222 3092.4
## - parent_marital_status:transport_means 3 608.0 75010 3092.7
## - gender:is_first_child 1 113.6 74516 3092.8
## - test_prep:transport_means 1 159.0 74561 3093.2
## - test_prep:practice_sport 2 417.4 74819 3093.2
## - gender:wkly_study_hours 2 418.8 74821 3093.2
## - test_prep:wkly_study_hours 2 435.0 74837 3093.3
## - is_first_child:transport_means 1 223.9 74626 3093.7
## - gender:practice_sport 2 478.2 74880 3093.7
## - lunch_type:is_first_child 1 250.2 74652 3093.9
## <none> 74402 3093.9
## - lunch_type:transport_means 1 305.0 74707 3094.3
## - parent_educ:practice_sport 10 2677.4 77079 3094.8
## - practice_sport:wkly_study_hours 4 1145.4 75547 3094.9
## - parent_educ:parent_marital_status 14 3963.2 78365 3096.5
## + parent_educ:is_first_child 5 908.9 73493 3096.7
## - ethnic_group:lunch_type 4 1401.7 75804 3096.9
## - ethnic_group:parent_marital_status 10 2988.4 77390 3097.1
## + practice_sport:is_first_child 2 89.6 74312 3097.2
## + lunch_type:parent_marital_status 3 333.8 74068 3097.2
## - lunch_type:wkly_study_hours 2 987.7 75390 3097.7
## - lunch_type:practice_sport 2 1005.9 75408 3097.8
## + gender:ethnic_group 4 468.2 73934 3098.2
## - ethnic_group:transport_means 4 1592.6 75995 3098.4
## + gender:parent_marital_status 3 140.4 74262 3098.8
## + parent_educ:transport_means 5 540.0 73862 3099.6
## + parent_marital_status:practice_sport 5 445.6 73956 3100.3
## + gender:parent_educ 5 357.5 74045 3101.1
## + ethnic_group:practice_sport 8 1093.6 73308 3101.2
## + parent_educ:test_prep 5 283.3 74119 3101.7
## + parent_educ:lunch_type 5 216.9 74185 3102.2
## + parent_educ:wkly_study_hours 10 1215.8 73186 3104.2
## + ethnic_group:wkly_study_hours 8 490.9 73911 3106.0
## - parent_marital_status:wkly_study_hours 5 2913.7 77316 3106.6
## - parent_marital_status:is_first_child 2 2779.0 77181 3111.5
## + ethnic_group:parent_educ 20 2651.5 71751 3112.5
##
## Step: AIC=3090.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 2 226.9 74745 3088.6
## - ethnic_group:test_prep 4 755.2 75273 3088.8
## - test_prep:is_first_child 1 3.6 74522 3088.8
## - gender:lunch_type 1 4.0 74522 3088.8
## - gender:transport_means 1 5.2 74523 3088.9
## - lunch_type:test_prep 1 20.2 74538 3089.0
## - transport_means:wkly_study_hours 2 276.9 74795 3089.0
## - practice_sport:transport_means 2 283.8 74802 3089.1
## - gender:test_prep 1 39.9 74558 3089.1
## - parent_marital_status:transport_means 3 560.5 75079 3089.2
## - gender:is_first_child 1 131.9 74650 3089.9
## - test_prep:practice_sport 2 389.2 74907 3089.9
## - ethnic_group:is_first_child 4 902.5 75421 3089.9
## - gender:wkly_study_hours 2 420.9 74939 3090.1
## - test_prep:transport_means 1 178.7 74697 3090.2
## - test_prep:wkly_study_hours 2 447.6 74966 3090.3
## - is_first_child:transport_means 1 207.2 74725 3090.5
## - gender:practice_sport 2 487.0 75005 3090.7
## <none> 74518 3090.8
## - lunch_type:is_first_child 1 281.2 74799 3091.0
## - lunch_type:transport_means 1 316.1 74834 3091.3
## - parent_educ:practice_sport 10 2637.3 77155 3091.3
## - practice_sport:wkly_study_hours 4 1218.6 75737 3092.4
## - ethnic_group:parent_marital_status 10 2949.1 77467 3093.7
## + is_first_child:wkly_study_hours 2 116.1 74402 3093.9
## - ethnic_group:lunch_type 4 1419.2 75937 3093.9
## + parent_educ:is_first_child 5 851.5 73667 3094.0
## + practice_sport:is_first_child 2 79.9 74438 3094.2
## - parent_educ:parent_marital_status 14 4073.8 78592 3094.2
## + lunch_type:parent_marital_status 3 325.4 74193 3094.2
## - lunch_type:wkly_study_hours 2 1008.5 75527 3094.8
## - ethnic_group:transport_means 4 1571.5 76090 3095.1
## + gender:ethnic_group 4 463.4 74055 3095.1
## - lunch_type:practice_sport 2 1106.6 75625 3095.5
## + gender:parent_marital_status 3 122.9 74395 3095.8
## + parent_educ:transport_means 5 533.4 73985 3096.6
## + parent_marital_status:practice_sport 5 480.3 74038 3097.0
## + gender:parent_educ 5 382.2 74136 3097.8
## + ethnic_group:practice_sport 8 1106.0 73412 3098.0
## + parent_educ:test_prep 5 252.5 74266 3098.8
## + parent_educ:lunch_type 5 226.9 74291 3099.0
## + parent_educ:wkly_study_hours 10 1196.3 73322 3101.3
## + ethnic_group:wkly_study_hours 8 531.7 73986 3102.6
## - parent_marital_status:wkly_study_hours 5 2935.4 77454 3103.6
## - parent_marital_status:is_first_child 2 2749.1 77267 3108.2
## + ethnic_group:parent_educ 20 2507.0 72011 3110.6
##
## Step: AIC=3088.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means + transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 0.0 74745 3086.6
## - gender:transport_means 1 3.1 74748 3086.6
## - gender:lunch_type 1 3.2 74748 3086.6
## - ethnic_group:test_prep 4 771.7 75517 3086.7
## - lunch_type:test_prep 1 19.0 74764 3086.8
## - transport_means:wkly_study_hours 2 274.1 75019 3086.8
## - practice_sport:transport_means 2 282.2 75027 3086.8
## - gender:test_prep 1 33.7 74779 3086.9
## - parent_marital_status:transport_means 3 637.6 75383 3087.6
## - gender:is_first_child 1 140.0 74885 3087.7
## - gender:wkly_study_hours 2 427.7 75173 3088.0
## - test_prep:practice_sport 2 430.9 75176 3088.0
## - test_prep:wkly_study_hours 2 443.8 75189 3088.1
## - is_first_child:transport_means 1 194.2 74939 3088.1
## - test_prep:transport_means 1 204.7 74950 3088.2
## - gender:practice_sport 2 473.1 75218 3088.3
## - ethnic_group:is_first_child 4 989.3 75734 3088.4
## <none> 74745 3088.6
## - lunch_type:is_first_child 1 262.7 75008 3088.7
## - parent_educ:practice_sport 10 2614.3 77359 3088.9
## - lunch_type:transport_means 1 313.3 75058 3089.1
## - ethnic_group:parent_marital_status 11 2935.6 77681 3089.3
## - parent_educ:parent_marital_status 15 4085.3 78830 3090.0
## - practice_sport:wkly_study_hours 4 1210.8 75956 3090.1
## + test_prep:parent_marital_status 2 226.9 74518 3090.8
## + is_first_child:wkly_study_hours 2 126.8 74618 3091.6
## + parent_educ:is_first_child 5 831.9 73913 3092.0
## + practice_sport:is_first_child 2 75.7 74669 3092.0
## - ethnic_group:lunch_type 4 1478.6 76224 3092.2
## + lunch_type:parent_marital_status 3 308.8 74436 3092.2
## - lunch_type:wkly_study_hours 2 1020.1 75765 3092.6
## - lunch_type:practice_sport 2 1054.2 75799 3092.9
## + gender:ethnic_group 4 446.6 74298 3093.1
## - ethnic_group:transport_means 4 1611.0 76356 3093.2
## + gender:parent_marital_status 3 127.1 74618 3093.6
## + parent_educ:transport_means 5 508.2 74237 3094.6
## + parent_marital_status:practice_sport 5 478.0 74267 3094.8
## + ethnic_group:practice_sport 8 1145.2 73600 3095.5
## + gender:parent_educ 5 370.5 74374 3095.7
## + parent_educ:lunch_type 5 254.2 74491 3096.6
## + parent_educ:test_prep 5 216.4 74529 3096.9
## + parent_educ:wkly_study_hours 10 1231.3 73514 3098.8
## + ethnic_group:wkly_study_hours 8 555.6 74189 3100.2
## - parent_marital_status:wkly_study_hours 6 3151.7 77897 3101.0
## - parent_marital_status:is_first_child 3 2970.8 77716 3105.6
## + ethnic_group:parent_educ 20 2580.0 72165 3107.9
##
## Step: AIC=3086.61
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 3.1 74748 3084.6
## - gender:lunch_type 1 3.2 74748 3084.6
## - ethnic_group:test_prep 4 773.4 75518 3084.7
## - lunch_type:test_prep 1 19.0 74764 3084.8
## - transport_means:wkly_study_hours 2 274.3 75019 3084.8
## - practice_sport:transport_means 2 282.1 75027 3084.8
## - gender:test_prep 1 33.7 74779 3084.9
## - parent_marital_status:transport_means 3 638.4 75383 3085.6
## - gender:is_first_child 1 140.6 74886 3085.7
## - gender:wkly_study_hours 2 429.3 75174 3086.0
## - test_prep:practice_sport 2 431.0 75176 3086.0
## - test_prep:wkly_study_hours 2 443.8 75189 3086.1
## - is_first_child:transport_means 1 194.3 74939 3086.1
## - test_prep:transport_means 1 204.7 74950 3086.2
## - gender:practice_sport 2 474.3 75219 3086.3
## - ethnic_group:is_first_child 4 990.3 75735 3086.4
## <none> 74745 3086.6
## - lunch_type:is_first_child 1 263.8 75009 3086.7
## - parent_educ:practice_sport 10 2614.7 77360 3086.9
## - lunch_type:transport_means 1 315.2 75060 3087.1
## - ethnic_group:parent_marital_status 11 2937.1 77682 3087.3
## - parent_educ:parent_marital_status 15 4085.4 78830 3088.0
## - practice_sport:wkly_study_hours 4 1213.1 75958 3088.1
## + test_prep:is_first_child 1 0.0 74745 3088.6
## + test_prep:parent_marital_status 2 223.3 74522 3088.8
## + is_first_child:wkly_study_hours 2 126.2 74619 3089.6
## + practice_sport:is_first_child 2 75.4 74670 3090.0
## + parent_educ:is_first_child 5 828.7 73916 3090.0
## + lunch_type:parent_marital_status 3 308.7 74436 3090.2
## - ethnic_group:lunch_type 4 1481.4 76226 3090.2
## - lunch_type:wkly_study_hours 2 1020.8 75766 3090.6
## - lunch_type:practice_sport 2 1055.5 75800 3090.9
## + gender:ethnic_group 4 446.6 74298 3091.1
## - ethnic_group:transport_means 4 1611.0 76356 3091.2
## + gender:parent_marital_status 3 126.9 74618 3091.6
## + parent_educ:transport_means 5 504.6 74240 3092.6
## + parent_marital_status:practice_sport 5 478.0 74267 3092.8
## + ethnic_group:practice_sport 8 1145.0 73600 3093.5
## + gender:parent_educ 5 369.4 74376 3093.7
## + parent_educ:lunch_type 5 254.2 74491 3094.6
## + parent_educ:test_prep 5 216.1 74529 3094.9
## + parent_educ:wkly_study_hours 10 1230.4 73515 3096.8
## + ethnic_group:wkly_study_hours 8 552.7 74192 3098.2
## - parent_marital_status:wkly_study_hours 6 3152.6 77898 3099.0
## - parent_marital_status:is_first_child 3 2971.0 77716 3103.6
## + ethnic_group:parent_educ 20 2568.1 72177 3106.0
##
## Step: AIC=3084.64
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:lunch_type +
## gender:test_prep + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 3.4 74751 3082.7
## - ethnic_group:test_prep 4 772.2 75520 3082.7
## - lunch_type:test_prep 1 19.4 74767 3082.8
## - transport_means:wkly_study_hours 2 274.4 75022 3082.8
## - practice_sport:transport_means 2 282.4 75030 3082.9
## - gender:test_prep 1 32.1 74780 3082.9
## - parent_marital_status:transport_means 3 637.5 75386 3083.7
## - gender:is_first_child 1 140.3 74888 3083.7
## - test_prep:practice_sport 2 430.3 75178 3084.0
## - gender:wkly_study_hours 2 430.5 75179 3084.0
## - test_prep:wkly_study_hours 2 443.4 75191 3084.1
## - is_first_child:transport_means 1 197.9 74946 3084.2
## - test_prep:transport_means 1 209.1 74957 3084.3
## - gender:practice_sport 2 476.3 75224 3084.4
## - ethnic_group:is_first_child 4 991.8 75740 3084.4
## <none> 74748 3084.6
## - lunch_type:is_first_child 1 261.5 75010 3084.7
## - parent_educ:practice_sport 10 2633.2 77381 3085.1
## - lunch_type:transport_means 1 319.1 75067 3085.2
## - ethnic_group:parent_marital_status 11 2959.1 77707 3085.5
## - parent_educ:parent_marital_status 15 4087.6 78836 3086.1
## - practice_sport:wkly_study_hours 4 1210.0 75958 3086.1
## + gender:transport_means 1 3.1 74745 3086.6
## + test_prep:is_first_child 1 0.0 74748 3086.6
## + test_prep:parent_marital_status 2 221.4 74527 3086.9
## + is_first_child:wkly_study_hours 2 128.0 74620 3087.6
## + practice_sport:is_first_child 2 76.0 74672 3088.0
## + parent_educ:is_first_child 5 823.7 73924 3088.1
## + lunch_type:parent_marital_status 3 311.0 74437 3088.2
## - ethnic_group:lunch_type 4 1480.1 76228 3088.2
## - lunch_type:wkly_study_hours 2 1018.3 75766 3088.6
## - lunch_type:practice_sport 2 1052.9 75801 3088.9
## + gender:ethnic_group 4 449.4 74299 3089.1
## - ethnic_group:transport_means 4 1611.1 76359 3089.2
## + gender:parent_marital_status 3 126.5 74622 3089.6
## + parent_educ:transport_means 5 503.5 74245 3090.7
## + parent_marital_status:practice_sport 5 479.0 74269 3090.8
## + ethnic_group:practice_sport 8 1137.2 73611 3091.6
## + gender:parent_educ 5 368.6 74379 3091.7
## + parent_educ:lunch_type 5 256.9 74491 3092.6
## + parent_educ:test_prep 5 215.5 74533 3092.9
## + parent_educ:wkly_study_hours 10 1202.3 73546 3095.1
## + ethnic_group:wkly_study_hours 8 551.9 74196 3096.3
## - parent_marital_status:wkly_study_hours 6 3151.6 77900 3097.0
## - parent_marital_status:is_first_child 3 2984.7 77733 3101.7
## + ethnic_group:parent_educ 20 2567.4 72181 3104.0
##
## Step: AIC=3082.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 771.6 75523 3080.7
## - transport_means:wkly_study_hours 2 273.4 75025 3080.8
## - lunch_type:test_prep 1 20.5 74772 3080.8
## - practice_sport:transport_means 2 284.4 75036 3080.9
## - gender:test_prep 1 31.3 74783 3080.9
## - parent_marital_status:transport_means 3 636.2 75388 3081.7
## - gender:is_first_child 1 140.5 74892 3081.8
## - gender:wkly_study_hours 2 428.0 75179 3082.0
## - test_prep:practice_sport 2 433.4 75185 3082.1
## - test_prep:wkly_study_hours 2 443.5 75195 3082.2
## - is_first_child:transport_means 1 195.4 74947 3082.2
## - test_prep:transport_means 1 211.2 74963 3082.3
## - gender:practice_sport 2 475.6 75227 3082.4
## - ethnic_group:is_first_child 4 989.2 75741 3082.4
## <none> 74751 3082.7
## - lunch_type:is_first_child 1 264.5 75016 3082.8
## - parent_educ:practice_sport 10 2629.9 77381 3083.1
## - lunch_type:transport_means 1 323.5 75075 3083.2
## - ethnic_group:parent_marital_status 11 2960.2 77712 3083.6
## - parent_educ:parent_marital_status 15 4086.7 78838 3084.1
## - practice_sport:wkly_study_hours 4 1215.8 75967 3084.2
## + gender:lunch_type 1 3.4 74748 3084.6
## + gender:transport_means 1 3.2 74748 3084.6
## + test_prep:is_first_child 1 0.0 74751 3084.7
## + test_prep:parent_marital_status 2 220.7 74531 3084.9
## + is_first_child:wkly_study_hours 2 127.3 74624 3085.7
## + practice_sport:is_first_child 2 74.4 74677 3086.1
## + parent_educ:is_first_child 5 822.7 73929 3086.1
## + lunch_type:parent_marital_status 3 314.3 74437 3086.2
## - ethnic_group:lunch_type 4 1480.8 76232 3086.2
## - lunch_type:wkly_study_hours 2 1015.8 75767 3086.6
## - lunch_type:practice_sport 2 1077.3 75829 3087.1
## + gender:ethnic_group 4 446.2 74305 3087.1
## - ethnic_group:transport_means 4 1620.2 76372 3087.3
## + gender:parent_marital_status 3 125.2 74626 3087.7
## + parent_educ:transport_means 5 506.3 74245 3088.7
## + parent_marital_status:practice_sport 5 479.0 74272 3088.9
## + ethnic_group:practice_sport 8 1127.4 73624 3089.7
## + gender:parent_educ 5 368.0 74383 3089.8
## + parent_educ:lunch_type 5 259.4 74492 3090.6
## + parent_educ:test_prep 5 213.8 74538 3091.0
## + parent_educ:wkly_study_hours 10 1201.5 73550 3093.1
## + ethnic_group:wkly_study_hours 8 551.4 74200 3094.3
## - parent_marital_status:wkly_study_hours 6 3192.1 77943 3095.3
## - parent_marital_status:is_first_child 3 2981.5 77733 3099.7
## + ethnic_group:parent_educ 20 2531.3 72220 3102.3
##
## Step: AIC=3080.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:test_prep + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 11.2 75534 3078.8
## - transport_means:wkly_study_hours 2 278.8 75802 3078.9
## - lunch_type:test_prep 1 35.1 75558 3079.0
## - practice_sport:transport_means 2 292.2 75815 3079.0
## - parent_marital_status:transport_means 3 569.2 76092 3079.2
## - gender:is_first_child 1 97.8 75621 3079.5
## - test_prep:practice_sport 2 392.1 75915 3079.8
## - gender:wkly_study_hours 2 415.8 75939 3080.0
## - is_first_child:transport_means 1 206.3 75729 3080.3
## - lunch_type:is_first_child 1 230.7 75754 3080.5
## - gender:practice_sport 2 488.1 76011 3080.5
## - test_prep:transport_means 1 243.1 75766 3080.6
## <none> 75523 3080.7
## - ethnic_group:is_first_child 4 1039.2 76562 3080.8
## - ethnic_group:parent_marital_status 11 2923.8 78447 3081.1
## - test_prep:wkly_study_hours 2 590.8 76114 3081.3
## - lunch_type:transport_means 1 353.3 75876 3081.5
## - parent_educ:practice_sport 10 2734.4 78257 3081.7
## - parent_educ:parent_marital_status 15 4073.2 79596 3081.7
## - practice_sport:wkly_study_hours 4 1215.7 76739 3082.1
## + ethnic_group:test_prep 4 771.6 74751 3082.7
## - ethnic_group:lunch_type 4 1286.4 76809 3082.7
## + gender:lunch_type 1 2.7 75520 3082.7
## + gender:transport_means 1 2.1 75521 3082.7
## + test_prep:is_first_child 1 1.5 75522 3082.7
## + test_prep:parent_marital_status 2 233.9 75289 3082.9
## + is_first_child:wkly_study_hours 2 112.4 75411 3083.8
## + parent_educ:is_first_child 5 859.8 74663 3084.0
## + practice_sport:is_first_child 2 84.3 75439 3084.1
## + lunch_type:parent_marital_status 3 334.5 75188 3084.1
## - lunch_type:wkly_study_hours 2 995.9 76519 3084.4
## - ethnic_group:transport_means 4 1599.8 77123 3085.1
## + gender:parent_marital_status 3 137.8 75385 3085.6
## - lunch_type:practice_sport 2 1217.2 76740 3086.2
## + gender:ethnic_group 4 290.9 75232 3086.4
## + parent_educ:transport_means 5 542.4 74981 3086.5
## + parent_marital_status:practice_sport 5 462.2 75061 3087.1
## + ethnic_group:practice_sport 8 1117.8 74405 3087.9
## + gender:parent_educ 5 330.2 75193 3088.1
## + parent_educ:lunch_type 5 277.0 75246 3088.6
## + parent_educ:test_prep 5 146.2 75377 3089.6
## + parent_educ:wkly_study_hours 10 1155.0 74368 3091.6
## - parent_marital_status:wkly_study_hours 6 3000.9 78524 3091.7
## + ethnic_group:wkly_study_hours 8 559.8 74963 3092.3
## - parent_marital_status:is_first_child 3 3061.0 78584 3098.2
## + ethnic_group:parent_educ 20 2514.4 73009 3100.7
##
## Step: AIC=3078.81
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means +
## transport_means:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 273.8 75808 3076.9
## - practice_sport:transport_means 2 292.1 75826 3077.1
## - lunch_type:test_prep 1 38.5 75573 3077.1
## - parent_marital_status:transport_means 3 575.3 76109 3077.3
## - gender:is_first_child 1 93.4 75627 3077.5
## - test_prep:practice_sport 2 389.8 75924 3077.8
## - gender:wkly_study_hours 2 432.6 75967 3078.2
## - is_first_child:transport_means 1 203.0 75737 3078.4
## - lunch_type:is_first_child 1 227.6 75762 3078.6
## - test_prep:transport_means 1 239.8 75774 3078.7
## - gender:practice_sport 2 500.9 76035 3078.7
## <none> 75534 3078.8
## - ethnic_group:is_first_child 4 1033.7 76568 3078.8
## - test_prep:wkly_study_hours 2 583.8 76118 3079.3
## - ethnic_group:parent_marital_status 11 2952.3 78486 3079.4
## - lunch_type:transport_means 1 358.4 75893 3079.6
## - parent_educ:parent_marital_status 15 4062.5 79597 3079.7
## - parent_educ:practice_sport 10 2755.3 78289 3079.9
## - practice_sport:wkly_study_hours 4 1211.3 76745 3080.2
## + gender:test_prep 1 11.2 75523 3080.7
## + gender:lunch_type 1 2.2 75532 3080.8
## - ethnic_group:lunch_type 4 1289.5 76824 3080.8
## + test_prep:is_first_child 1 1.4 75533 3080.8
## + gender:transport_means 1 1.2 75533 3080.8
## + ethnic_group:test_prep 4 751.4 74783 3080.9
## + test_prep:parent_marital_status 2 229.3 75305 3081.0
## + is_first_child:wkly_study_hours 2 113.7 75420 3081.9
## + parent_educ:is_first_child 5 858.1 74676 3082.1
## + practice_sport:is_first_child 2 86.3 75448 3082.1
## + lunch_type:parent_marital_status 3 338.3 75196 3082.2
## - lunch_type:wkly_study_hours 2 1005.4 76540 3082.6
## - ethnic_group:transport_means 4 1607.5 77142 3083.2
## + gender:parent_marital_status 3 142.5 75392 3083.7
## - lunch_type:practice_sport 2 1211.6 76746 3084.2
## + gender:ethnic_group 4 285.8 75248 3084.6
## + parent_educ:transport_means 5 532.2 75002 3084.6
## + parent_marital_status:practice_sport 5 465.2 75069 3085.2
## + ethnic_group:practice_sport 8 1103.3 74431 3086.1
## + gender:parent_educ 5 323.0 75211 3086.3
## + parent_educ:lunch_type 5 280.5 75254 3086.6
## + parent_educ:test_prep 5 151.5 75383 3087.6
## + parent_educ:wkly_study_hours 10 1155.9 74378 3089.7
## - parent_marital_status:wkly_study_hours 6 2990.8 78525 3089.7
## + ethnic_group:wkly_study_hours 8 568.8 74965 3090.3
## - parent_marital_status:is_first_child 3 3050.1 78584 3096.2
## + ethnic_group:parent_educ 20 2513.7 73020 3098.8
##
## Step: AIC=3076.94
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:test_prep + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 37.1 75845 3075.2
## - parent_marital_status:transport_means 3 554.6 76363 3075.2
## - practice_sport:transport_means 2 311.7 76120 3075.4
## - gender:is_first_child 1 96.6 75905 3075.7
## - gender:wkly_study_hours 2 407.4 76215 3076.1
## - test_prep:practice_sport 2 424.4 76232 3076.2
## - is_first_child:transport_means 1 201.9 76010 3076.5
## - test_prep:transport_means 1 209.2 76017 3076.6
## - lunch_type:is_first_child 1 237.9 76046 3076.8
## - gender:practice_sport 2 498.4 76306 3076.8
## - ethnic_group:parent_marital_status 11 2879.7 78688 3076.9
## <none> 75808 3076.9
## - ethnic_group:is_first_child 4 1044.5 76852 3077.0
## - parent_educ:practice_sport 10 2625.6 78434 3077.0
## - test_prep:wkly_study_hours 2 530.9 76339 3077.1
## - parent_educ:parent_marital_status 15 4007.1 79815 3077.3
## - lunch_type:transport_means 1 332.9 76141 3077.5
## - practice_sport:wkly_study_hours 4 1234.7 77043 3078.5
## + transport_means:wkly_study_hours 2 273.8 75534 3078.8
## + gender:test_prep 1 6.2 75802 3078.9
## + gender:lunch_type 1 1.6 75806 3078.9
## + gender:transport_means 1 1.5 75806 3078.9
## - ethnic_group:lunch_type 4 1295.3 77103 3078.9
## + test_prep:is_first_child 1 0.3 75808 3078.9
## + ethnic_group:test_prep 4 760.2 75048 3079.0
## + test_prep:parent_marital_status 2 236.2 75572 3079.1
## + is_first_child:wkly_study_hours 2 128.6 75679 3079.9
## + lunch_type:parent_marital_status 3 366.5 75441 3080.1
## + parent_educ:is_first_child 5 860.6 74947 3080.2
## + practice_sport:is_first_child 2 86.9 75721 3080.3
## - lunch_type:wkly_study_hours 2 1028.6 76837 3080.9
## + gender:parent_marital_status 3 127.2 75681 3081.9
## - ethnic_group:transport_means 4 1734.7 77543 3082.3
## - lunch_type:practice_sport 2 1215.6 77024 3082.3
## + gender:ethnic_group 4 306.9 75501 3082.6
## + parent_educ:transport_means 5 551.3 75257 3082.6
## + parent_marital_status:practice_sport 5 473.7 75334 3083.2
## + ethnic_group:practice_sport 8 1130.4 74677 3084.1
## + gender:parent_educ 5 343.9 75464 3084.3
## + parent_educ:lunch_type 5 307.8 75500 3084.5
## + parent_educ:test_prep 5 146.0 75662 3085.8
## + parent_educ:wkly_study_hours 10 1197.1 74611 3087.6
## - parent_marital_status:wkly_study_hours 6 3056.3 78864 3088.3
## + ethnic_group:wkly_study_hours 8 470.4 75338 3089.3
## - parent_marital_status:is_first_child 3 2949.0 78757 3093.5
## + ethnic_group:parent_educ 20 2520.2 73288 3097.0
##
## Step: AIC=3075.23
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:transport_means +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 560.4 76405 3073.6
## - practice_sport:transport_means 2 322.3 76167 3073.7
## - gender:is_first_child 1 101.3 75946 3074.0
## - gender:wkly_study_hours 2 403.5 76249 3074.4
## - test_prep:practice_sport 2 429.6 76275 3074.6
## - is_first_child:transport_means 1 190.4 76035 3074.7
## - test_prep:transport_means 1 208.1 76053 3074.8
## - gender:practice_sport 2 491.6 76337 3075.0
## - ethnic_group:parent_marital_status 11 2862.4 78707 3075.1
## - lunch_type:is_first_child 1 242.6 76088 3075.1
## <none> 75845 3075.2
## - test_prep:wkly_study_hours 2 526.9 76372 3075.3
## - ethnic_group:is_first_child 4 1053.8 76899 3075.4
## - parent_educ:practice_sport 10 2648.9 78494 3075.5
## - lunch_type:transport_means 1 311.6 76157 3075.7
## - parent_educ:parent_marital_status 15 4021.2 79866 3075.7
## + lunch_type:test_prep 1 37.1 75808 3076.9
## - practice_sport:wkly_study_hours 4 1266.5 77111 3077.0
## + transport_means:wkly_study_hours 2 272.4 75573 3077.1
## + gender:test_prep 1 8.6 75836 3077.2
## + ethnic_group:test_prep 4 772.6 75072 3077.2
## + gender:lunch_type 1 2.6 75842 3077.2
## + gender:transport_means 1 1.9 75843 3077.2
## + test_prep:is_first_child 1 0.4 75845 3077.2
## + test_prep:parent_marital_status 2 236.9 75608 3077.4
## - ethnic_group:lunch_type 4 1340.5 77186 3077.6
## + is_first_child:wkly_study_hours 2 137.2 75708 3078.2
## + lunch_type:parent_marital_status 3 366.8 75478 3078.4
## + practice_sport:is_first_child 2 91.2 75754 3078.5
## + parent_educ:is_first_child 5 842.0 75003 3078.7
## - lunch_type:wkly_study_hours 2 1005.4 76850 3079.0
## + gender:parent_marital_status 3 121.2 75724 3080.3
## - lunch_type:practice_sport 2 1201.8 77047 3080.5
## - ethnic_group:transport_means 4 1735.4 77580 3080.6
## + gender:ethnic_group 4 317.8 75527 3080.8
## + parent_educ:transport_means 5 567.5 75278 3080.8
## + parent_marital_status:practice_sport 5 467.7 75377 3081.6
## + ethnic_group:practice_sport 8 1157.3 74688 3082.2
## + gender:parent_educ 5 355.3 75490 3082.5
## + parent_educ:lunch_type 5 301.9 75543 3082.9
## + parent_educ:test_prep 5 144.0 75701 3084.1
## + parent_educ:wkly_study_hours 10 1215.6 74629 3085.7
## - parent_marital_status:wkly_study_hours 6 3086.6 78932 3086.8
## + ethnic_group:wkly_study_hours 8 482.4 75363 3087.5
## - parent_marital_status:is_first_child 3 2971.6 78817 3091.9
## + ethnic_group:parent_educ 20 2528.3 73317 3095.2
##
## Step: AIC=3073.57
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 289.2 76695 3071.8
## - gender:is_first_child 1 104.0 76509 3072.4
## - parent_educ:parent_marital_status 15 3830.4 80236 3072.4
## - gender:wkly_study_hours 2 397.3 76803 3072.6
## - test_prep:practice_sport 2 408.6 76814 3072.7
## - ethnic_group:parent_marital_status 11 2815.5 79221 3072.9
## - gender:practice_sport 2 469.1 76875 3073.2
## - test_prep:transport_means 1 227.5 76633 3073.3
## - lunch_type:is_first_child 1 235.1 76640 3073.4
## - test_prep:wkly_study_hours 2 513.5 76919 3073.5
## <none> 76405 3073.6
## - ethnic_group:is_first_child 4 1050.0 77455 3073.6
## - is_first_child:transport_means 1 266.4 76672 3073.6
## - lunch_type:transport_means 1 334.7 76740 3074.2
## - parent_educ:practice_sport 10 2736.7 79142 3074.3
## - practice_sport:wkly_study_hours 4 1246.9 77652 3075.1
## + test_prep:parent_marital_status 2 308.7 76097 3075.2
## + parent_marital_status:transport_means 3 560.4 75845 3075.2
## + lunch_type:test_prep 1 42.8 76363 3075.2
## + gender:test_prep 1 14.8 76391 3075.5
## + gender:lunch_type 1 1.2 76404 3075.6
## + gender:transport_means 1 1.0 76404 3075.6
## + test_prep:is_first_child 1 0.1 76405 3075.6
## + transport_means:wkly_study_hours 2 249.8 76156 3075.6
## - ethnic_group:lunch_type 4 1321.6 77727 3075.7
## + ethnic_group:test_prep 4 702.7 75703 3076.1
## + lunch_type:parent_marital_status 3 361.0 76044 3076.8
## + is_first_child:wkly_study_hours 2 83.7 76322 3076.9
## + practice_sport:is_first_child 2 61.6 76344 3077.1
## - lunch_type:wkly_study_hours 2 1054.0 77459 3077.7
## - ethnic_group:transport_means 4 1591.6 77997 3077.7
## + parent_educ:is_first_child 5 718.4 75687 3078.0
## + gender:parent_marital_status 3 187.7 76218 3078.1
## + gender:ethnic_group 4 335.7 76070 3079.0
## - lunch_type:practice_sport 2 1274.9 77680 3079.3
## + parent_educ:transport_means 5 466.6 75939 3080.0
## + parent_marital_status:practice_sport 5 458.2 75947 3080.0
## + ethnic_group:practice_sport 8 1209.6 75196 3080.2
## + gender:parent_educ 5 401.7 76004 3080.5
## + parent_educ:lunch_type 5 307.1 76098 3081.2
## + parent_educ:test_prep 5 119.6 76286 3082.7
## - parent_marital_status:wkly_study_hours 6 2935.7 79341 3083.8
## + parent_educ:wkly_study_hours 10 1232.7 75173 3084.0
## + ethnic_group:wkly_study_hours 8 494.3 75911 3085.8
## - parent_marital_status:is_first_child 3 3121.7 79527 3091.2
## + ethnic_group:parent_educ 20 2414.4 73991 3094.6
##
## Step: AIC=3071.8
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:parent_marital_status +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 15 3742.3 80437 3069.9
## - ethnic_group:parent_marital_status 11 2688.4 79383 3070.1
## - test_prep:practice_sport 2 378.6 77073 3070.7
## - gender:is_first_child 1 134.4 76829 3070.8
## - gender:wkly_study_hours 2 415.0 77109 3071.0
## - gender:practice_sport 2 415.5 77110 3071.0
## - test_prep:transport_means 1 209.1 76904 3071.4
## - lunch_type:is_first_child 1 249.4 76944 3071.7
## - ethnic_group:is_first_child 4 1038.9 77733 3071.7
## - test_prep:wkly_study_hours 2 514.3 77209 3071.8
## <none> 76695 3071.8
## - parent_educ:practice_sport 10 2659.6 79354 3071.9
## - is_first_child:transport_means 1 324.1 77019 3072.3
## - lunch_type:transport_means 1 352.1 77047 3072.5
## - practice_sport:wkly_study_hours 4 1213.3 77908 3073.1
## + test_prep:parent_marital_status 2 318.9 76376 3073.3
## + lunch_type:test_prep 1 53.6 76641 3073.4
## + practice_sport:transport_means 2 289.2 76405 3073.6
## - ethnic_group:lunch_type 4 1283.1 77978 3073.6
## + gender:test_prep 1 15.0 76680 3073.7
## + transport_means:wkly_study_hours 2 270.1 76424 3073.7
## + parent_marital_status:transport_means 3 527.2 76167 3073.7
## + gender:lunch_type 1 2.2 76692 3073.8
## + gender:transport_means 1 1.1 76693 3073.8
## + test_prep:is_first_child 1 0.2 76694 3073.8
## + ethnic_group:test_prep 4 713.2 75981 3074.3
## + lunch_type:parent_marital_status 3 359.8 76335 3075.0
## + is_first_child:wkly_study_hours 2 90.4 76604 3075.1
## + practice_sport:is_first_child 2 60.5 76634 3075.3
## - lunch_type:wkly_study_hours 2 1032.8 77727 3075.7
## - ethnic_group:transport_means 4 1618.0 78313 3076.1
## + parent_educ:is_first_child 5 721.0 75974 3076.2
## + gender:parent_marital_status 3 164.7 76530 3076.5
## + gender:ethnic_group 4 328.7 76366 3077.3
## - lunch_type:practice_sport 2 1255.8 77950 3077.4
## + parent_marital_status:practice_sport 5 444.6 76250 3078.4
## + ethnic_group:practice_sport 8 1203.1 75491 3078.5
## + parent_educ:transport_means 5 422.0 76273 3078.6
## + gender:parent_educ 5 396.2 76298 3078.8
## + parent_educ:lunch_type 5 370.5 76324 3078.9
## + parent_educ:test_prep 5 141.0 76554 3080.7
## - parent_marital_status:wkly_study_hours 6 2936.1 79631 3082.0
## + parent_educ:wkly_study_hours 10 1143.1 75551 3082.9
## + ethnic_group:wkly_study_hours 8 499.7 76195 3083.9
## - parent_marital_status:is_first_child 3 3103.2 79798 3089.2
## + ethnic_group:parent_educ 20 2362.4 74332 3093.3
##
## Step: AIC=3069.91
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:practice_sport +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 252.6 80689 3067.8
## - ethnic_group:is_first_child 4 845.9 81283 3068.1
## - gender:wkly_study_hours 2 337.8 80775 3068.4
## - ethnic_group:lunch_type 4 964.9 81402 3068.9
## - gender:is_first_child 1 152.4 80589 3069.0
## - gender:practice_sport 2 443.1 80880 3069.2
## - test_prep:wkly_study_hours 2 487.4 80924 3069.5
## <none> 80437 3069.9
## - is_first_child:transport_means 1 291.8 80729 3070.1
## - ethnic_group:parent_marital_status 11 3119.9 83557 3070.4
## - test_prep:transport_means 1 338.9 80776 3070.4
## - practice_sport:wkly_study_hours 4 1165.6 81602 3070.4
## - lunch_type:is_first_child 1 392.2 80829 3070.8
## - lunch_type:transport_means 1 419.3 80856 3071.0
## - parent_educ:practice_sport 10 2963.0 83400 3071.2
## + lunch_type:test_prep 1 63.2 80374 3071.4
## + parent_educ:parent_marital_status 15 3742.3 76695 3071.8
## + gender:transport_means 1 14.0 80423 3071.8
## + gender:lunch_type 1 1.8 80435 3071.9
## + gender:test_prep 1 1.5 80435 3071.9
## + test_prep:is_first_child 1 0.2 80437 3071.9
## + transport_means:wkly_study_hours 2 233.9 80203 3072.2
## + practice_sport:transport_means 2 201.1 80236 3072.4
## + is_first_child:wkly_study_hours 2 171.6 80265 3072.7
## + ethnic_group:test_prep 4 689.7 79747 3072.8
## + parent_marital_status:transport_means 3 369.7 80067 3073.2
## + lunch_type:parent_marital_status 3 335.5 80101 3073.4
## + practice_sport:is_first_child 2 26.1 80411 3073.7
## + test_prep:parent_marital_status 3 293.2 80144 3073.8
## + parent_educ:is_first_child 5 730.0 79707 3074.5
## - ethnic_group:transport_means 4 1749.2 82186 3074.6
## + gender:ethnic_group 4 429.6 80007 3074.8
## - lunch_type:practice_sport 2 1226.7 81664 3074.8
## + gender:parent_educ 5 654.3 79783 3075.1
## - lunch_type:wkly_study_hours 2 1303.3 81740 3075.4
## + parent_marital_status:practice_sport 6 872.2 79565 3075.5
## + gender:parent_marital_status 3 19.2 80418 3075.8
## + parent_educ:transport_means 5 433.9 80003 3076.7
## + parent_educ:lunch_type 5 383.9 80053 3077.1
## + ethnic_group:practice_sport 8 1150.9 79286 3077.4
## - parent_marital_status:wkly_study_hours 6 2787.1 83224 3078.0
## + parent_educ:wkly_study_hours 10 1534.7 78902 3078.6
## + parent_educ:test_prep 5 161.9 80275 3078.7
## + ethnic_group:wkly_study_hours 8 363.2 80074 3083.2
## - parent_marital_status:is_first_child 3 3025.4 83462 3085.7
## + ethnic_group:parent_educ 20 2639.7 77797 3090.2
##
## Step: AIC=3067.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:is_first_child +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 317.4 81007 3066.1
## - ethnic_group:is_first_child 4 876.0 81565 3066.1
## - gender:is_first_child 1 149.2 80839 3066.8
## - ethnic_group:lunch_type 4 1028.7 81718 3067.2
## - test_prep:wkly_study_hours 2 478.9 81168 3067.2
## - gender:practice_sport 2 482.9 81172 3067.3
## <none> 80689 3067.8
## - is_first_child:transport_means 1 301.4 80991 3068.0
## - ethnic_group:parent_marital_status 11 3122.9 83812 3068.2
## - test_prep:transport_means 1 362.3 81052 3068.4
## - practice_sport:wkly_study_hours 4 1204.8 81894 3068.5
## - lunch_type:transport_means 1 401.7 81091 3068.7
## - lunch_type:is_first_child 1 414.9 81104 3068.8
## - parent_educ:practice_sport 10 2989.8 83679 3069.2
## + lunch_type:test_prep 1 68.9 80620 3069.3
## + gender:transport_means 1 16.0 80673 3069.6
## + gender:lunch_type 1 3.0 80686 3069.7
## + gender:test_prep 1 0.9 80689 3069.8
## + test_prep:is_first_child 1 0.5 80689 3069.8
## + test_prep:practice_sport 2 252.6 80437 3069.9
## + transport_means:wkly_study_hours 2 250.9 80439 3069.9
## + practice_sport:transport_means 2 179.0 80510 3070.4
## + parent_educ:parent_marital_status 15 3616.3 77073 3070.7
## + is_first_child:wkly_study_hours 2 142.8 80547 3070.7
## + ethnic_group:test_prep 4 679.6 80010 3070.8
## + parent_marital_status:transport_means 3 354.1 80335 3071.2
## + lunch_type:parent_marital_status 3 344.3 80345 3071.2
## + test_prep:parent_marital_status 3 342.7 80347 3071.2
## + practice_sport:is_first_child 2 29.2 80660 3071.6
## + parent_educ:is_first_child 5 816.0 79873 3071.8
## - ethnic_group:transport_means 4 1694.6 82384 3072.0
## + gender:parent_educ 5 703.6 79986 3072.6
## + gender:ethnic_group 4 422.9 80266 3072.7
## + parent_marital_status:practice_sport 6 896.9 79792 3073.2
## - lunch_type:practice_sport 2 1303.1 81992 3073.2
## + gender:parent_marital_status 3 35.1 80654 3073.5
## - lunch_type:wkly_study_hours 2 1383.7 82073 3073.8
## + parent_educ:transport_means 5 451.8 80238 3074.4
## + parent_educ:lunch_type 5 429.1 80260 3074.6
## - parent_marital_status:wkly_study_hours 6 2769.9 83459 3075.7
## + ethnic_group:practice_sport 8 1090.2 79599 3075.7
## + parent_educ:wkly_study_hours 10 1608.6 79081 3075.9
## + parent_educ:test_prep 5 143.5 80546 3076.7
## + ethnic_group:wkly_study_hours 8 358.2 80331 3081.1
## - parent_marital_status:is_first_child 3 3049.0 83738 3083.6
## + ethnic_group:parent_educ 20 2713.0 77976 3087.6
##
## Step: AIC=3066.08
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## parent_educ:practice_sport + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 824.9 81832 3064.1
## - gender:is_first_child 1 157.3 81164 3065.2
## - test_prep:wkly_study_hours 2 469.7 81477 3065.5
## - ethnic_group:lunch_type 4 1034.1 82041 3065.6
## - gender:practice_sport 2 527.0 81534 3065.9
## - is_first_child:transport_means 1 270.8 81278 3066.1
## <none> 81007 3066.1
## - ethnic_group:parent_marital_status 11 3080.5 84087 3066.1
## - practice_sport:wkly_study_hours 4 1177.4 82184 3066.6
## - test_prep:transport_means 1 371.6 81378 3066.8
## - lunch_type:is_first_child 1 398.6 81405 3067.0
## - lunch_type:transport_means 1 411.4 81418 3067.1
## + lunch_type:test_prep 1 65.7 80941 3067.6
## + gender:wkly_study_hours 2 317.4 80689 3067.8
## - parent_educ:practice_sport 10 3056.9 84064 3067.9
## + gender:transport_means 1 14.9 80992 3068.0
## + gender:test_prep 1 6.9 81000 3068.0
## + test_prep:is_first_child 1 4.0 81003 3068.1
## + gender:lunch_type 1 1.5 81005 3068.1
## + test_prep:practice_sport 2 232.2 80775 3068.4
## + transport_means:wkly_study_hours 2 227.6 80779 3068.4
## + practice_sport:transport_means 2 188.6 80818 3068.7
## + is_first_child:wkly_study_hours 2 133.4 80873 3069.1
## + ethnic_group:test_prep 4 673.4 80333 3069.2
## + test_prep:parent_marital_status 3 361.5 80645 3069.4
## + parent_marital_status:transport_means 3 350.5 80656 3069.5
## + parent_educ:parent_marital_status 15 3542.0 77465 3069.7
## + practice_sport:is_first_child 2 23.4 80983 3069.9
## + lunch_type:parent_marital_status 3 291.6 80715 3069.9
## - ethnic_group:transport_means 4 1664.0 82671 3070.1
## + parent_educ:is_first_child 5 765.7 80241 3070.5
## + gender:ethnic_group 4 458.3 80549 3070.7
## + gender:parent_educ 5 716.2 80291 3070.8
## - lunch_type:wkly_study_hours 2 1298.7 82306 3071.5
## + parent_marital_status:practice_sport 6 903.1 80104 3071.5
## - lunch_type:practice_sport 2 1320.2 82327 3071.6
## + gender:parent_marital_status 3 51.8 80955 3071.7
## + parent_educ:transport_means 5 408.3 80598 3073.1
## + parent_educ:wkly_study_hours 10 1753.4 79253 3073.2
## + parent_educ:lunch_type 5 387.2 80620 3073.2
## + ethnic_group:practice_sport 8 1147.0 79860 3073.7
## + parent_educ:test_prep 5 166.8 80840 3074.9
## - parent_marital_status:wkly_study_hours 6 3058.9 84066 3075.9
## + ethnic_group:wkly_study_hours 8 326.3 80680 3079.7
## - parent_marital_status:is_first_child 3 2917.4 83924 3080.9
## + ethnic_group:parent_educ 20 2718.5 78288 3085.9
##
## Step: AIC=3064.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 852.1 82684 3062.2
## - ethnic_group:parent_marital_status 11 2845.2 84677 3062.2
## - test_prep:wkly_study_hours 2 337.2 82169 3062.5
## - gender:is_first_child 1 92.9 81925 3062.7
## - is_first_child:transport_means 1 144.4 81976 3063.1
## - gender:practice_sport 2 513.8 82346 3063.8
## <none> 81832 3064.1
## - test_prep:transport_means 1 331.1 82163 3064.4
## - lunch_type:transport_means 1 353.6 82185 3064.6
## - practice_sport:wkly_study_hours 4 1203.5 83035 3064.7
## + lunch_type:test_prep 1 70.7 81761 3065.6
## - parent_educ:practice_sport 10 3037.2 84869 3065.6
## - lunch_type:is_first_child 1 516.8 82349 3065.8
## + test_prep:is_first_child 1 12.1 81820 3066.0
## + gender:transport_means 1 11.6 81820 3066.0
## + gender:test_prep 1 3.5 81828 3066.0
## + gender:lunch_type 1 1.2 81830 3066.1
## + ethnic_group:is_first_child 4 824.9 81007 3066.1
## + test_prep:practice_sport 2 268.1 81564 3066.1
## + gender:wkly_study_hours 2 266.2 81565 3066.1
## + transport_means:wkly_study_hours 2 249.9 81582 3066.2
## + is_first_child:wkly_study_hours 2 194.0 81638 3066.7
## + practice_sport:transport_means 2 186.5 81645 3066.7
## + ethnic_group:test_prep 4 728.6 81103 3066.8
## + test_prep:parent_marital_status 3 433.6 81398 3066.9
## + parent_marital_status:transport_means 3 351.9 81480 3067.5
## + practice_sport:is_first_child 2 25.3 81806 3067.9
## + lunch_type:parent_marital_status 3 240.0 81592 3068.3
## + parent_educ:is_first_child 5 786.2 81046 3068.4
## + gender:ethnic_group 4 454.0 81378 3068.8
## - lunch_type:wkly_study_hours 2 1224.7 83056 3068.8
## + gender:parent_educ 5 703.5 81128 3069.0
## + parent_educ:parent_marital_status 15 3382.9 78449 3069.2
## - lunch_type:practice_sport 2 1335.5 83167 3069.6
## + parent_marital_status:practice_sport 6 882.2 80950 3069.7
## - ethnic_group:transport_means 4 1911.7 83743 3069.7
## + gender:parent_marital_status 3 35.0 81797 3069.8
## + parent_educ:wkly_study_hours 10 1830.4 80001 3070.7
## + parent_educ:transport_means 5 445.2 81387 3070.8
## + parent_educ:lunch_type 5 377.7 81454 3071.3
## + ethnic_group:practice_sport 8 1069.7 80762 3072.3
## + parent_educ:test_prep 5 160.9 81671 3072.9
## - parent_marital_status:wkly_study_hours 6 2994.3 84826 3073.3
## - parent_marital_status:is_first_child 3 2566.9 84399 3076.3
## + ethnic_group:wkly_study_hours 8 354.1 81478 3077.5
## + ethnic_group:parent_educ 20 2784.5 79047 3083.6
##
## Step: AIC=3062.17
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:parent_marital_status +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 11 2792.28 85476 3059.8
## - test_prep:wkly_study_hours 2 332.30 83016 3060.5
## - gender:is_first_child 1 84.77 82769 3060.8
## - is_first_child:transport_means 1 122.86 82807 3061.0
## - gender:practice_sport 2 436.01 83120 3061.3
## - practice_sport:wkly_study_hours 4 1064.27 83748 3061.7
## <none> 82684 3062.2
## - test_prep:transport_means 1 367.25 83051 3062.8
## - lunch_type:transport_means 1 416.94 83101 3063.1
## + lunch_type:test_prep 1 106.82 82577 3063.4
## - lunch_type:is_first_child 1 457.20 83141 3063.4
## + test_prep:practice_sport 2 327.08 82357 3063.8
## - parent_educ:practice_sport 10 3101.14 85785 3063.9
## + ethnic_group:lunch_type 4 852.14 81832 3064.1
## + gender:transport_means 1 14.86 82669 3064.1
## + test_prep:is_first_child 1 5.78 82678 3064.1
## + gender:lunch_type 1 5.44 82678 3064.1
## + gender:test_prep 1 4.70 82679 3064.1
## + gender:wkly_study_hours 2 272.64 82411 3064.2
## + transport_means:wkly_study_hours 2 254.90 82429 3064.3
## + is_first_child:wkly_study_hours 2 193.27 82491 3064.8
## + test_prep:parent_marital_status 3 449.82 82234 3064.9
## + practice_sport:transport_means 2 155.79 82528 3065.1
## + ethnic_group:is_first_child 4 642.90 82041 3065.6
## + parent_marital_status:transport_means 3 349.67 82334 3065.7
## + practice_sport:is_first_child 2 33.45 82650 3065.9
## + ethnic_group:test_prep 4 566.41 82117 3066.1
## + parent_educ:is_first_child 5 839.05 81845 3066.2
## - lunch_type:wkly_study_hours 2 1133.23 83817 3066.2
## + lunch_type:parent_marital_status 3 269.52 82414 3066.2
## + gender:ethnic_group 4 456.00 82228 3066.9
## - ethnic_group:transport_means 4 1846.35 84530 3067.2
## + parent_marital_status:practice_sport 6 954.98 81729 3067.3
## + gender:parent_educ 5 616.92 82067 3067.8
## + gender:parent_marital_status 3 37.83 82646 3067.9
## + parent_educ:transport_means 5 525.02 82159 3068.4
## - lunch_type:practice_sport 2 1543.54 84227 3069.1
## + parent_educ:parent_marital_status 15 3130.53 79553 3069.4
## + ethnic_group:practice_sport 8 1213.72 81470 3069.4
## + parent_educ:lunch_type 5 340.93 82343 3069.7
## + parent_educ:test_prep 5 161.91 82522 3071.0
## + parent_educ:wkly_study_hours 10 1527.60 81156 3071.2
## - parent_marital_status:wkly_study_hours 6 3050.50 85734 3071.5
## - parent_marital_status:is_first_child 3 2646.16 85330 3074.8
## + ethnic_group:wkly_study_hours 8 326.65 82357 3075.8
## + ethnic_group:parent_educ 20 2852.94 79831 3081.4
##
## Step: AIC=3059.76
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## gender:is_first_child + ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 99.6 85576 3058.4
## - practice_sport:wkly_study_hours 4 1008.6 86485 3058.7
## - test_prep:wkly_study_hours 2 479.0 85955 3059.1
## - is_first_child:transport_means 1 198.2 85674 3059.1
## - gender:practice_sport 2 564.4 86041 3059.7
## <none> 85476 3059.8
## - lunch_type:is_first_child 1 308.3 85784 3059.9
## - parent_educ:practice_sport 10 2978.9 88455 3060.0
## - test_prep:transport_means 1 364.2 85840 3060.3
## - lunch_type:transport_means 1 417.7 85894 3060.6
## + test_prep:practice_sport 2 328.5 85148 3061.5
## + lunch_type:test_prep 1 32.5 85444 3061.5
## + gender:test_prep 1 14.8 85461 3061.7
## + test_prep:is_first_child 1 1.7 85474 3061.8
## + gender:lunch_type 1 0.3 85476 3061.8
## + gender:transport_means 1 0.0 85476 3061.8
## + transport_means:wkly_study_hours 2 244.4 85232 3062.1
## + gender:wkly_study_hours 2 237.4 85239 3062.1
## + ethnic_group:parent_marital_status 11 2792.3 82684 3062.2
## + ethnic_group:lunch_type 4 799.3 84677 3062.2
## + practice_sport:transport_means 2 103.1 85373 3063.1
## + parent_marital_status:transport_means 3 372.4 85104 3063.2
## - lunch_type:wkly_study_hours 2 1083.0 86559 3063.2
## + is_first_child:wkly_study_hours 2 80.1 85396 3063.2
## + lunch_type:parent_marital_status 3 364.8 85111 3063.2
## + test_prep:parent_marital_status 3 353.5 85123 3063.3
## + parent_educ:parent_marital_status 15 3706.0 81770 3063.6
## + practice_sport:is_first_child 2 15.9 85460 3063.7
## - ethnic_group:transport_means 4 1765.3 87241 3063.8
## + ethnic_group:test_prep 4 491.6 84985 3064.4
## + parent_marital_status:practice_sport 6 1039.9 84436 3064.5
## + parent_educ:is_first_child 5 744.1 84732 3064.6
## + gender:parent_marital_status 3 152.7 85323 3064.7
## + ethnic_group:is_first_child 4 412.6 85064 3064.9
## + gender:ethnic_group 4 376.8 85099 3065.2
## - parent_marital_status:wkly_study_hours 6 2624.6 88101 3065.6
## + parent_educ:transport_means 5 566.9 84909 3065.8
## + parent_educ:wkly_study_hours 10 1851.9 83624 3066.8
## + gender:parent_educ 5 421.5 85055 3066.8
## + ethnic_group:practice_sport 8 1241.8 84234 3067.1
## - lunch_type:practice_sport 2 1699.0 87175 3067.4
## + parent_educ:lunch_type 5 306.9 85169 3067.6
## - parent_marital_status:is_first_child 3 2204.5 87681 3068.8
## + parent_educ:test_prep 5 128.8 85347 3068.9
## + ethnic_group:wkly_study_hours 8 315.5 85161 3073.6
## + ethnic_group:parent_educ 20 2736.0 82740 3080.6
##
## Step: AIC=3058.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + practice_sport:wkly_study_hours +
## is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 466.5 86042 3057.7
## - practice_sport:wkly_study_hours 4 1055.8 86632 3057.7
## - is_first_child:transport_means 1 187.3 85763 3057.7
## - lunch_type:is_first_child 1 290.5 85866 3058.4
## <none> 85576 3058.4
## - gender:practice_sport 2 587.3 86163 3058.5
## - test_prep:transport_means 1 362.2 85938 3058.9
## - parent_educ:practice_sport 10 3073.1 88649 3059.3
## - lunch_type:transport_means 1 454.6 86030 3059.6
## + gender:is_first_child 1 99.6 85476 3059.8
## + lunch_type:test_prep 1 36.7 85539 3060.2
## + test_prep:practice_sport 2 321.6 85254 3060.2
## + gender:test_prep 1 10.1 85566 3060.4
## + test_prep:is_first_child 1 3.9 85572 3060.4
## + gender:lunch_type 1 0.3 85575 3060.4
## + gender:transport_means 1 0.0 85576 3060.4
## + ethnic_group:parent_marital_status 11 2807.1 82769 3060.8
## + gender:wkly_study_hours 2 239.8 85336 3060.8
## + transport_means:wkly_study_hours 2 235.6 85340 3060.8
## + ethnic_group:lunch_type 4 790.3 84785 3061.0
## + practice_sport:transport_means 2 119.8 85456 3061.6
## - lunch_type:wkly_study_hours 2 1069.3 86645 3061.8
## + is_first_child:wkly_study_hours 2 93.1 85483 3061.8
## + parent_marital_status:transport_means 3 378.6 85197 3061.8
## + lunch_type:parent_marital_status 3 373.1 85203 3061.9
## + test_prep:parent_marital_status 3 366.2 85210 3061.9
## + practice_sport:is_first_child 2 17.0 85559 3062.3
## + parent_educ:parent_marital_status 15 3677.7 81898 3062.5
## - ethnic_group:transport_means 4 1832.9 87409 3062.9
## + ethnic_group:test_prep 4 469.5 85106 3063.2
## + parent_educ:is_first_child 5 746.7 84829 3063.3
## + gender:parent_marital_status 3 164.8 85411 3063.3
## + parent_marital_status:practice_sport 6 1021.0 84555 3063.4
## + gender:ethnic_group 4 396.7 85179 3063.7
## - parent_marital_status:wkly_study_hours 6 2559.8 88136 3063.8
## + ethnic_group:is_first_child 4 373.2 85203 3063.9
## + parent_educ:transport_means 5 547.7 85028 3064.7
## + parent_educ:wkly_study_hours 10 1883.7 83692 3065.3
## + gender:parent_educ 5 423.0 85153 3065.5
## + parent_educ:lunch_type 5 345.4 85230 3066.1
## + ethnic_group:practice_sport 8 1193.1 84383 3066.2
## - lunch_type:practice_sport 2 1747.0 87323 3066.4
## - parent_marital_status:is_first_child 3 2145.8 87722 3067.1
## + parent_educ:test_prep 5 132.8 85443 3067.5
## + ethnic_group:wkly_study_hours 8 314.1 85262 3072.3
## + ethnic_group:parent_educ 20 2622.3 82953 3080.1
##
## Step: AIC=3057.66
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours + is_first_child:transport_means
##
## Df Sum of Sq RSS AIC
## - is_first_child:transport_means 1 180.8 86223 3056.9
## - practice_sport:wkly_study_hours 4 1089.4 87132 3057.1
## - parent_educ:practice_sport 10 2918.5 88961 3057.3
## - lunch_type:is_first_child 1 245.9 86288 3057.3
## - gender:practice_sport 2 569.1 86611 3057.6
## <none> 86042 3057.7
## - test_prep:transport_means 1 322.8 86365 3057.9
## - lunch_type:transport_means 1 347.8 86390 3058.0
## + test_prep:wkly_study_hours 2 466.5 85576 3058.4
## + ethnic_group:parent_marital_status 11 2953.0 83089 3059.1
## + gender:is_first_child 1 87.1 85955 3059.1
## + lunch_type:test_prep 1 28.5 86014 3059.5
## + test_prep:practice_sport 2 315.9 85726 3059.5
## + gender:test_prep 1 3.7 86039 3059.6
## + test_prep:is_first_child 1 2.4 86040 3059.6
## + gender:lunch_type 1 0.5 86042 3059.7
## + gender:transport_means 1 0.1 86042 3059.7
## + gender:wkly_study_hours 2 231.2 85811 3060.1
## + transport_means:wkly_study_hours 2 203.4 85839 3060.3
## + ethnic_group:lunch_type 4 765.9 85276 3060.4
## + practice_sport:transport_means 2 121.1 85921 3060.8
## + is_first_child:wkly_study_hours 2 80.3 85962 3061.1
## + parent_marital_status:transport_means 3 367.4 85675 3061.1
## + test_prep:parent_marital_status 3 353.3 85689 3061.2
## + lunch_type:parent_marital_status 3 351.9 85690 3061.2
## - lunch_type:wkly_study_hours 2 1130.2 87172 3061.4
## + practice_sport:is_first_child 2 22.1 86020 3061.5
## - ethnic_group:transport_means 4 1762.4 87805 3061.6
## + ethnic_group:test_prep 4 563.0 85479 3061.8
## + parent_educ:parent_marital_status 15 3637.1 82405 3062.2
## + parent_educ:is_first_child 5 782.3 85260 3062.3
## + parent_marital_status:practice_sport 6 1062.0 84980 3062.3
## + gender:parent_marital_status 3 132.6 85910 3062.8
## + gender:ethnic_group 4 414.5 85628 3062.8
## - parent_marital_status:wkly_study_hours 6 2558.9 88601 3062.9
## + parent_educ:wkly_study_hours 10 2045.6 83997 3063.5
## + parent_educ:transport_means 5 565.0 85477 3063.8
## + ethnic_group:is_first_child 4 274.4 85768 3063.8
## + gender:parent_educ 5 469.8 85572 3064.4
## - lunch_type:practice_sport 2 1596.3 87639 3064.5
## + parent_educ:lunch_type 5 353.9 85688 3065.2
## + ethnic_group:practice_sport 8 1091.5 84951 3066.1
## - parent_marital_status:is_first_child 3 2170.7 88213 3066.4
## + parent_educ:test_prep 5 135.1 85907 3066.7
## + ethnic_group:wkly_study_hours 8 351.6 85691 3071.2
## + ethnic_group:parent_educ 20 2649.4 83393 3079.2
##
## Step: AIC=3056.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + parent_educ:practice_sport +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 2832.5 89055 3056.0
## - practice_sport:wkly_study_hours 4 1063.9 87287 3056.1
## - lunch_type:is_first_child 1 244.7 86468 3056.6
## <none> 86223 3056.9
## - gender:practice_sport 2 601.5 86825 3057.0
## - lunch_type:transport_means 1 345.2 86568 3057.2
## - test_prep:transport_means 1 351.2 86574 3057.3
## + is_first_child:transport_means 1 180.8 86042 3057.7
## + test_prep:wkly_study_hours 2 459.9 85763 3057.7
## + ethnic_group:parent_marital_status 11 3020.0 83203 3057.9
## + gender:is_first_child 1 77.2 86146 3058.4
## + test_prep:practice_sport 2 317.0 85906 3058.7
## + lunch_type:test_prep 1 18.6 86204 3058.8
## + test_prep:is_first_child 1 4.4 86219 3058.9
## + gender:test_prep 1 2.5 86221 3058.9
## + gender:transport_means 1 1.6 86221 3058.9
## + gender:lunch_type 1 0.0 86223 3058.9
## + gender:wkly_study_hours 2 214.7 86008 3059.4
## + transport_means:wkly_study_hours 2 201.8 86021 3059.5
## + ethnic_group:lunch_type 4 760.6 85462 3059.7
## + practice_sport:transport_means 2 138.2 86085 3059.9
## + parent_marital_status:transport_means 3 425.2 85798 3060.0
## + is_first_child:wkly_study_hours 2 66.5 86156 3060.4
## + test_prep:parent_marital_status 3 354.6 85868 3060.5
## + lunch_type:parent_marital_status 3 348.9 85874 3060.5
## + practice_sport:is_first_child 2 15.4 86208 3060.8
## - ethnic_group:transport_means 4 1773.5 87996 3060.9
## + ethnic_group:test_prep 4 562.5 85660 3061.0
## - lunch_type:wkly_study_hours 2 1200.3 87423 3061.1
## + parent_educ:is_first_child 5 810.7 85412 3061.3
## + parent_educ:parent_marital_status 15 3644.1 82579 3061.4
## + parent_marital_status:practice_sport 6 1060.8 85162 3061.6
## + gender:ethnic_group 4 447.2 85776 3061.8
## - parent_marital_status:wkly_study_hours 6 2529.8 88753 3062.0
## + gender:parent_marital_status 3 115.9 86107 3062.1
## + parent_educ:wkly_study_hours 10 2054.9 84168 3062.7
## + parent_educ:transport_means 5 527.1 85696 3063.3
## - lunch_type:practice_sport 2 1567.4 87790 3063.5
## + ethnic_group:is_first_child 4 198.1 86025 3063.5
## + gender:parent_educ 5 456.3 85767 3063.8
## + parent_educ:lunch_type 5 338.7 85884 3064.6
## + ethnic_group:practice_sport 8 1146.4 85077 3065.0
## - parent_marital_status:is_first_child 3 2120.8 88344 3065.2
## + parent_educ:test_prep 5 168.1 86055 3065.7
## + ethnic_group:wkly_study_hours 8 368.5 85854 3070.4
## + ethnic_group:parent_educ 20 2575.7 83647 3079.0
##
## Step: AIC=3055.97
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## practice_sport:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 914.5 89970 3054.0
## - gender:practice_sport 2 409.2 89465 3054.7
## - lunch_type:is_first_child 1 155.2 89211 3055.0
## <none> 89055 3056.0
## - lunch_type:transport_means 1 306.2 89362 3056.0
## - test_prep:transport_means 1 380.6 89436 3056.5
## + gender:is_first_child 1 165.2 88890 3056.9
## + parent_educ:practice_sport 10 2832.5 86223 3056.9
## + is_first_child:transport_means 1 94.7 88961 3057.3
## + lunch_type:test_prep 1 36.5 89019 3057.7
## + gender:test_prep 1 19.6 89036 3057.8
## + gender:transport_means 1 16.0 89039 3057.9
## + test_prep:wkly_study_hours 2 307.5 88748 3057.9
## + gender:lunch_type 1 5.0 89050 3057.9
## + test_prep:is_first_child 1 2.3 89053 3057.9
## + gender:wkly_study_hours 2 281.6 88774 3058.1
## + test_prep:practice_sport 2 274.1 88781 3058.2
## + parent_marital_status:transport_means 3 536.1 88519 3058.4
## + parent_educ:is_first_child 5 1120.5 87935 3058.5
## + ethnic_group:parent_marital_status 11 2866.7 86189 3058.7
## + parent_educ:parent_marital_status 15 4025.6 85030 3058.7
## + practice_sport:transport_means 2 128.4 88927 3059.1
## + ethnic_group:lunch_type 4 727.7 88328 3059.1
## + transport_means:wkly_study_hours 2 91.2 88964 3059.4
## + test_prep:parent_marital_status 3 363.7 88692 3059.6
## + is_first_child:wkly_study_hours 2 59.9 88996 3059.6
## - parent_marital_status:wkly_study_hours 6 2422.9 91478 3059.8
## - lunch_type:wkly_study_hours 2 1192.1 90248 3059.8
## + ethnic_group:test_prep 4 620.7 88435 3059.8
## + practice_sport:is_first_child 2 13.6 89042 3059.9
## + lunch_type:parent_marital_status 3 260.3 88795 3060.2
## - ethnic_group:transport_means 4 1888.2 90944 3060.3
## - lunch_type:practice_sport 2 1306.9 90362 3060.6
## + gender:ethnic_group 4 493.9 88561 3060.7
## + gender:parent_marital_status 3 188.4 88867 3060.7
## + parent_educ:wkly_study_hours 10 2257.7 86798 3060.8
## + parent_marital_status:practice_sport 6 871.7 88184 3062.2
## + ethnic_group:is_first_child 4 259.4 88796 3062.2
## + parent_educ:transport_means 5 535.3 88520 3062.4
## + ethnic_group:practice_sport 8 1361.2 87694 3062.9
## + gender:parent_educ 5 452.5 88603 3063.0
## - parent_marital_status:is_first_child 3 2116.2 91172 3063.8
## + parent_educ:lunch_type 5 311.0 88744 3063.9
## + parent_educ:test_prep 5 246.7 88809 3064.3
## + ethnic_group:wkly_study_hours 8 414.2 88641 3069.2
## + ethnic_group:parent_educ 20 2184.6 86871 3081.3
## - parent_educ 5 6212.6 95268 3085.8
##
## Step: AIC=3053.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 104.8 90075 3052.7
## - gender:practice_sport 2 480.0 90450 3053.1
## - lunch_type:transport_means 1 253.2 90223 3053.7
## <none> 89970 3054.0
## - test_prep:transport_means 1 362.9 90333 3054.4
## + gender:is_first_child 1 220.7 89749 3054.5
## + is_first_child:transport_means 1 78.8 89891 3055.5
## + lunch_type:test_prep 1 55.0 89915 3055.6
## + test_prep:wkly_study_hours 2 329.5 89640 3055.8
## + gender:test_prep 1 17.9 89952 3055.9
## + test_prep:is_first_child 1 8.8 89961 3055.9
## + gender:transport_means 1 6.2 89964 3055.9
## + practice_sport:wkly_study_hours 4 914.5 89055 3056.0
## + gender:lunch_type 1 3.0 89967 3056.0
## + test_prep:practice_sport 2 288.9 89681 3056.1
## + parent_educ:practice_sport 10 2683.0 87287 3056.1
## + gender:wkly_study_hours 2 260.5 89709 3056.3
## + parent_marital_status:transport_means 3 536.5 89433 3056.5
## - ethnic_group:transport_means 4 1731.1 91701 3057.2
## + transport_means:wkly_study_hours 2 106.2 89864 3057.3
## + practice_sport:transport_means 2 105.7 89864 3057.3
## + is_first_child:wkly_study_hours 2 105.5 89864 3057.3
## - lunch_type:wkly_study_hours 2 1121.3 91091 3057.3
## + parent_educ:parent_marital_status 15 3959.8 86010 3057.4
## + parent_educ:is_first_child 5 962.3 89008 3057.7
## + ethnic_group:parent_marital_status 11 2751.1 87219 3057.7
## + test_prep:parent_marital_status 3 339.8 89630 3057.8
## + ethnic_group:test_prep 4 625.2 89345 3057.9
## + practice_sport:is_first_child 2 16.4 89954 3057.9
## + ethnic_group:lunch_type 4 613.6 89356 3058.0
## - lunch_type:practice_sport 2 1223.0 91193 3058.0
## + gender:ethnic_group 4 541.3 89429 3058.4
## - parent_marital_status:wkly_study_hours 6 2566.6 92537 3058.6
## + gender:parent_marital_status 3 213.7 89756 3058.6
## + lunch_type:parent_marital_status 3 185.9 89784 3058.8
## + parent_educ:wkly_study_hours 10 2163.2 87807 3059.6
## + ethnic_group:is_first_child 4 308.4 89662 3060.0
## + parent_educ:transport_means 5 606.4 89364 3060.0
## + parent_marital_status:practice_sport 6 804.4 89166 3060.7
## + gender:parent_educ 5 467.2 89503 3060.9
## + ethnic_group:practice_sport 8 1351.5 88618 3061.1
## - parent_marital_status:is_first_child 3 2027.1 91997 3061.1
## + parent_educ:lunch_type 5 369.3 89601 3061.6
## + parent_educ:test_prep 5 264.7 89705 3062.3
## + ethnic_group:wkly_study_hours 8 442.1 89528 3067.1
## + ethnic_group:parent_educ 20 2078.3 87892 3080.2
## - parent_educ 5 6298.3 96268 3083.9
##
## Step: AIC=3052.68
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + gender:practice_sport +
## ethnic_group:transport_means + lunch_type:practice_sport +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## test_prep:transport_means + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 526.0 90601 3052.1
## - lunch_type:transport_means 1 243.3 90318 3052.3
## <none> 90075 3052.7
## - test_prep:transport_means 1 340.3 90415 3052.9
## + gender:is_first_child 1 202.2 89873 3053.3
## + lunch_type:is_first_child 1 104.8 89970 3054.0
## + is_first_child:transport_means 1 77.3 89997 3054.2
## + lunch_type:test_prep 1 62.2 90012 3054.3
## + gender:test_prep 1 14.6 90060 3054.6
## + test_prep:is_first_child 1 11.9 90063 3054.6
## + gender:transport_means 1 3.2 90072 3054.7
## + gender:lunch_type 1 2.1 90073 3054.7
## + test_prep:wkly_study_hours 2 305.6 89769 3054.7
## + test_prep:practice_sport 2 299.1 89776 3054.7
## + practice_sport:wkly_study_hours 4 864.0 89211 3055.0
## + gender:wkly_study_hours 2 256.1 89819 3055.0
## + parent_marital_status:transport_means 3 532.3 89542 3055.2
## + parent_educ:practice_sport 10 2607.2 87468 3055.3
## + parent_educ:parent_marital_status 15 4009.3 86065 3055.8
## + is_first_child:wkly_study_hours 2 126.1 89949 3055.8
## - ethnic_group:transport_means 4 1728.8 91804 3055.9
## + transport_means:wkly_study_hours 2 113.9 89961 3055.9
## + practice_sport:transport_means 2 112.5 89962 3055.9
## - lunch_type:wkly_study_hours 2 1152.6 91227 3056.2
## + test_prep:parent_marital_status 3 350.7 89724 3056.4
## + parent_educ:is_first_child 5 948.3 89126 3056.4
## - lunch_type:practice_sport 2 1201.6 91276 3056.5
## + practice_sport:is_first_child 2 20.0 90055 3056.6
## + ethnic_group:lunch_type 4 607.8 89467 3056.7
## + ethnic_group:test_prep 4 594.8 89480 3056.8
## + gender:ethnic_group 4 554.4 89520 3057.0
## + ethnic_group:parent_marital_status 11 2638.8 87436 3057.1
## + gender:parent_marital_status 3 203.9 89871 3057.3
## + lunch_type:parent_marital_status 3 174.4 89900 3057.5
## - parent_marital_status:wkly_study_hours 6 2636.8 92712 3057.7
## + ethnic_group:is_first_child 4 345.1 89730 3058.4
## + parent_educ:wkly_study_hours 10 2142.9 87932 3058.5
## + parent_educ:transport_means 5 600.4 89474 3058.7
## + gender:parent_educ 5 465.6 89609 3059.6
## + ethnic_group:practice_sport 8 1357.1 88718 3059.7
## + parent_marital_status:practice_sport 6 716.6 89358 3060.0
## - parent_marital_status:is_first_child 3 2113.0 92188 3060.4
## + parent_educ:lunch_type 5 343.3 89731 3060.4
## + parent_educ:test_prep 5 264.1 89811 3060.9
## + ethnic_group:wkly_study_hours 8 452.4 89622 3065.7
## + ethnic_group:parent_educ 20 2115.9 87959 3078.7
## - parent_educ 5 6269.5 96344 3082.4
##
## Step: AIC=3052.12
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 262.4 90863 3051.8
## <none> 90601 3052.1
## - test_prep:transport_means 1 326.9 90928 3052.2
## + gender:practice_sport 2 526.0 90075 3052.7
## + gender:is_first_child 1 218.3 90382 3052.7
## + lunch_type:is_first_child 1 150.8 90450 3053.1
## + is_first_child:transport_means 1 90.8 90510 3053.5
## + lunch_type:test_prep 1 63.7 90537 3053.7
## + gender:test_prep 1 21.3 90579 3054.0
## + test_prep:practice_sport 2 327.6 90273 3054.0
## + practice_sport:wkly_study_hours 4 930.4 89670 3054.0
## + gender:transport_means 1 8.0 90593 3054.1
## + test_prep:is_first_child 1 7.2 90594 3054.1
## + gender:lunch_type 1 2.4 90598 3054.1
## + test_prep:wkly_study_hours 2 303.1 90298 3054.1
## + gender:wkly_study_hours 2 298.6 90302 3054.2
## + parent_marital_status:transport_means 3 501.6 90099 3054.8
## + parent_educ:parent_marital_status 15 4059.5 86541 3055.1
## + transport_means:wkly_study_hours 2 140.5 90460 3055.2
## + is_first_child:wkly_study_hours 2 130.1 90471 3055.3
## - ethnic_group:transport_means 4 1762.1 92363 3055.5
## + practice_sport:transport_means 2 85.4 90515 3055.6
## - lunch_type:wkly_study_hours 2 1156.5 91757 3055.6
## + parent_educ:is_first_child 5 955.4 89645 3055.9
## + ethnic_group:parent_marital_status 11 2757.1 87844 3055.9
## + test_prep:parent_marital_status 3 340.6 90260 3055.9
## + practice_sport:is_first_child 2 14.2 90587 3056.0
## - lunch_type:practice_sport 2 1234.5 91835 3056.1
## + ethnic_group:test_prep 4 608.3 89992 3056.1
## + parent_educ:practice_sport 10 2370.5 88230 3056.5
## + ethnic_group:lunch_type 4 550.1 90051 3056.5
## - parent_marital_status:wkly_study_hours 6 2560.9 93162 3056.6
## + gender:ethnic_group 4 526.6 90074 3056.7
## + gender:parent_marital_status 3 213.9 90387 3056.7
## + lunch_type:parent_marital_status 3 164.7 90436 3057.0
## + ethnic_group:is_first_child 4 357.4 90243 3057.8
## + parent_educ:transport_means 5 589.9 90011 3058.3
## + ethnic_group:practice_sport 8 1489.7 89111 3058.3
## + parent_educ:wkly_study_hours 10 2057.4 88543 3058.6
## + gender:parent_educ 5 482.3 90118 3059.0
## - parent_marital_status:is_first_child 3 2053.4 92654 3059.3
## + parent_marital_status:practice_sport 6 723.2 89878 3059.4
## + parent_educ:lunch_type 5 389.3 90212 3059.6
## + parent_educ:test_prep 5 259.3 90341 3060.4
## + ethnic_group:wkly_study_hours 8 436.2 90165 3065.3
## + ethnic_group:parent_educ 20 2189.7 88411 3077.7
## - parent_educ 5 6278.7 96879 3081.7
## - gender 1 8889.6 99490 3105.3
##
## Step: AIC=3051.82
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## test_prep:transport_means + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 300.1 91163 3051.8
## <none> 90863 3051.8
## + lunch_type:transport_means 1 262.4 90601 3052.1
## + gender:is_first_child 1 254.3 90609 3052.2
## + gender:practice_sport 2 545.1 90318 3052.3
## + lunch_type:is_first_child 1 138.9 90724 3052.9
## + is_first_child:transport_means 1 89.3 90774 3053.2
## + lunch_type:test_prep 1 40.2 90823 3053.6
## + gender:test_prep 1 27.3 90836 3053.6
## + test_prep:is_first_child 1 16.5 90847 3053.7
## + gender:transport_means 1 13.3 90850 3053.7
## + test_prep:practice_sport 2 311.6 90551 3053.8
## + gender:lunch_type 1 0.7 90862 3053.8
## + gender:wkly_study_hours 2 303.7 90559 3053.8
## + practice_sport:wkly_study_hours 4 876.1 89987 3054.1
## + test_prep:wkly_study_hours 2 231.4 90632 3054.3
## + parent_marital_status:transport_means 3 501.6 90362 3054.6
## + parent_educ:parent_marital_status 15 4074.5 86789 3054.8
## + transport_means:wkly_study_hours 2 135.8 90727 3054.9
## + is_first_child:wkly_study_hours 2 130.2 90733 3055.0
## - ethnic_group:transport_means 4 1751.0 92614 3055.1
## - lunch_type:wkly_study_hours 2 1125.4 91989 3055.1
## + practice_sport:transport_means 2 93.8 90769 3055.2
## - lunch_type:practice_sport 2 1176.8 92040 3055.4
## + test_prep:parent_marital_status 3 352.3 90511 3055.5
## + ethnic_group:parent_marital_status 11 2754.8 88108 3055.7
## + practice_sport:is_first_child 2 18.0 90845 3055.7
## + parent_educ:is_first_child 5 919.1 89944 3055.8
## + ethnic_group:test_prep 4 595.6 90267 3055.9
## + ethnic_group:lunch_type 4 591.5 90272 3056.0
## + gender:parent_marital_status 3 236.6 90627 3056.3
## - parent_marital_status:wkly_study_hours 6 2586.1 93449 3056.4
## + parent_educ:practice_sport 10 2339.6 88524 3056.4
## + gender:ethnic_group 4 509.1 90354 3056.5
## + lunch_type:parent_marital_status 3 183.6 90680 3056.6
## + ethnic_group:is_first_child 4 324.0 90539 3057.7
## + parent_educ:transport_means 5 598.1 90265 3057.9
## + gender:parent_educ 5 547.4 90316 3058.3
## + parent_educ:wkly_study_hours 10 2035.7 88827 3058.4
## + ethnic_group:practice_sport 8 1397.2 89466 3058.7
## + parent_marital_status:practice_sport 6 746.8 90116 3058.9
## - parent_marital_status:is_first_child 3 2062.9 92926 3059.1
## + parent_educ:lunch_type 5 398.6 90465 3059.2
## + parent_educ:test_prep 5 285.8 90577 3060.0
## + ethnic_group:wkly_study_hours 8 399.8 90463 3065.2
## + ethnic_group:parent_educ 20 2151.2 88712 3077.7
## - parent_educ 5 6148.1 97011 3080.4
## - gender 1 8826.3 99689 3104.5
##
## Step: AIC=3051.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours
##
## Df Sum of Sq RSS AIC
## <none> 91163 3051.8
## + test_prep:transport_means 1 300.1 90863 3051.8
## + gender:is_first_child 1 257.6 90906 3052.1
## + lunch_type:transport_means 1 235.6 90928 3052.2
## + gender:practice_sport 2 530.8 90632 3052.3
## + lunch_type:is_first_child 1 114.5 91049 3053.0
## + is_first_child:transport_means 1 108.6 91055 3053.1
## + lunch_type:test_prep 1 42.2 91121 3053.5
## + gender:transport_means 1 24.2 91139 3053.6
## + gender:test_prep 1 23.3 91140 3053.6
## + test_prep:is_first_child 1 18.2 91145 3053.7
## + test_prep:practice_sport 2 325.8 90837 3053.7
## + gender:wkly_study_hours 2 322.6 90841 3053.7
## + gender:lunch_type 1 0.0 91163 3053.8
## + practice_sport:wkly_study_hours 4 872.4 90291 3054.1
## + parent_educ:parent_marital_status 15 4174.7 86989 3054.1
## - lunch_type:wkly_study_hours 2 997.2 92160 3054.2
## + parent_marital_status:transport_means 3 537.0 90626 3054.3
## + test_prep:wkly_study_hours 2 211.0 90952 3054.4
## + is_first_child:wkly_study_hours 2 140.3 91023 3054.9
## + transport_means:wkly_study_hours 2 101.6 91062 3055.1
## + practice_sport:transport_means 2 92.2 91071 3055.2
## + test_prep:parent_marital_status 3 391.9 90771 3055.2
## - lunch_type:practice_sport 2 1208.9 92372 3055.5
## + parent_educ:is_first_child 5 948.5 90215 3055.6
## + ethnic_group:parent_marital_status 11 2759.5 88404 3055.6
## + practice_sport:is_first_child 2 16.4 91147 3055.7
## + ethnic_group:lunch_type 4 617.0 90546 3055.8
## - ethnic_group:transport_means 4 1874.3 93037 3055.8
## - parent_marital_status:wkly_study_hours 6 2516.2 93679 3055.8
## + ethnic_group:test_prep 4 578.0 90585 3056.0
## + gender:parent_marital_status 3 248.6 90915 3056.2
## + parent_educ:practice_sport 10 2364.5 88799 3056.3
## + gender:ethnic_group 4 528.5 90635 3056.3
## + lunch_type:parent_marital_status 3 187.1 90976 3056.6
## + ethnic_group:is_first_child 4 297.7 90866 3057.8
## + parent_educ:transport_means 5 601.1 90562 3057.9
## + gender:parent_educ 5 541.0 90622 3058.3
## + ethnic_group:practice_sport 8 1451.3 89712 3058.3
## + parent_educ:wkly_study_hours 10 2050.0 89113 3058.3
## + parent_marital_status:practice_sport 6 769.8 90393 3058.8
## + parent_educ:lunch_type 5 420.7 90743 3059.0
## - parent_marital_status:is_first_child 3 2087.3 93251 3059.1
## + parent_educ:test_prep 5 312.8 90850 3059.7
## + ethnic_group:wkly_study_hours 8 406.7 90757 3065.1
## + ethnic_group:parent_educ 20 2088.9 89074 3078.1
## - test_prep 1 4865.5 96029 3080.4
## - parent_educ 5 6366.3 97530 3081.6
## - gender 1 8627.7 99791 3103.1summary(stepwise_model_read)##
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
## lunch_type:practice_sport + lunch_type:wkly_study_hours +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours,
## data = df_4_mdl_read)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.540 -8.273 -0.267 9.481 33.728
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 64.0126 5.6402 11.349
## gendermale -7.9731 1.1041 -7.221
## ethnic_groupgroup B 4.0052 3.7361 1.072
## ethnic_groupgroup C 4.5817 3.4195 1.340
## ethnic_groupgroup D 4.6170 3.5000 1.319
## ethnic_groupgroup E 13.9574 3.8663 3.610
## parent_educbachelor's degree 3.3736 1.9408 1.738
## parent_educhigh school -5.9247 1.6817 -3.523
## parent_educmaster's degree 3.4397 2.4234 1.419
## parent_educsome college -2.3224 1.6870 -1.377
## parent_educsome high school -5.3232 1.6969 -3.137
## lunch_typestandard 2.0599 3.8020 0.542
## test_prepnone -6.2162 1.1463 -5.423
## parent_marital_statusmarried 10.2557 4.0650 2.523
## parent_marital_statussingle -0.8882 4.4420 -0.200
## parent_marital_statuswidowed 17.2457 10.8292 1.593
## practice_sportregularly -4.4245 3.2294 -1.370
## practice_sportsometimes -5.4217 3.1279 -1.733
## is_first_childyes 8.8087 3.3685 2.615
## transport_meansschool_bus 7.1540 3.8499 1.858
## wkly_study_hours> 10 -15.1280 5.0552 -2.993
## wkly_study_hours10-May 1.2358 3.6575 0.338
## ethnic_groupgroup B:transport_meansschool_bus -8.5078 4.6456 -1.831
## ethnic_groupgroup C:transport_meansschool_bus -8.7787 4.3480 -2.019
## ethnic_groupgroup D:transport_meansschool_bus -2.4914 4.4269 -0.563
## ethnic_groupgroup E:transport_meansschool_bus -12.1513 4.8881 -2.486
## lunch_typestandard:practice_sportregularly 4.3134 3.9100 1.103
## lunch_typestandard:practice_sportsometimes 9.0693 3.8110 2.380
## lunch_typestandard:wkly_study_hours> 10 6.1827 3.4568 1.789
## lunch_typestandard:wkly_study_hours10-May -1.3341 2.6912 -0.496
## parent_marital_statusmarried:is_first_childyes -10.3012 3.6911 -2.791
## parent_marital_statussingle:is_first_childyes -2.7153 4.1037 -0.662
## parent_marital_statuswidowed:is_first_childyes -11.5351 8.6888 -1.328
## parent_marital_statusmarried:wkly_study_hours> 10 11.8333 4.9161 2.407
## parent_marital_statussingle:wkly_study_hours> 10 20.4572 5.5006 3.719
## parent_marital_statuswidowed:wkly_study_hours> 10 5.7848 14.3577 0.403
## parent_marital_statusmarried:wkly_study_hours10-May 1.7018 3.6640 0.464
## parent_marital_statussingle:wkly_study_hours10-May 5.0455 4.1368 1.220
## parent_marital_statuswidowed:wkly_study_hours10-May -3.6043 10.7836 -0.334
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## gendermale 1.72e-12 ***
## ethnic_groupgroup B 0.284174
## ethnic_groupgroup C 0.180841
## ethnic_groupgroup D 0.187673
## ethnic_groupgroup E 0.000334 ***
## parent_educbachelor's degree 0.082717 .
## parent_educhigh school 0.000462 ***
## parent_educmaster's degree 0.156352
## parent_educsome college 0.169188
## parent_educsome high school 0.001798 **
## lunch_typestandard 0.588175
## test_prepnone 8.79e-08 ***
## parent_marital_statusmarried 0.011918 *
## parent_marital_statussingle 0.841585
## parent_marital_statuswidowed 0.111840
## practice_sportregularly 0.171222
## practice_sportsometimes 0.083598 .
## is_first_childyes 0.009167 **
## transport_meansschool_bus 0.063672 .
## wkly_study_hours> 10 0.002890 **
## wkly_study_hours10-May 0.735589
## ethnic_groupgroup B:transport_meansschool_bus 0.067585 .
## ethnic_groupgroup C:transport_meansschool_bus 0.043967 *
## ethnic_groupgroup D:transport_meansschool_bus 0.573809
## ethnic_groupgroup E:transport_meansschool_bus 0.013218 *
## lunch_typestandard:practice_sportregularly 0.270437
## lunch_typestandard:practice_sportsometimes 0.017661 *
## lunch_typestandard:wkly_study_hours> 10 0.074233 .
## lunch_typestandard:wkly_study_hours10-May 0.620296
## parent_marital_statusmarried:is_first_childyes 0.005440 **
## parent_marital_statussingle:is_first_childyes 0.508448
## parent_marital_statuswidowed:is_first_childyes 0.184867
## parent_marital_statusmarried:wkly_study_hours> 10 0.016410 *
## parent_marital_statussingle:wkly_study_hours> 10 0.000220 ***
## parent_marital_statuswidowed:wkly_study_hours> 10 0.687173
## parent_marital_statusmarried:wkly_study_hours10-May 0.642503
## parent_marital_statussingle:wkly_study_hours10-May 0.223116
## parent_marital_statuswidowed:wkly_study_hours10-May 0.738324
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.86 on 551 degrees of freedom
## Multiple R-squared: 0.3254, Adjusted R-squared: 0.2789
## F-statistic: 6.995 on 38 and 551 DF, p-value: < 2.2e-16Diagnostics
Writing
plot(stepwise_model_write)
step_as_lm_write=lm(formula = writing_score ~ gender + ethnic_group + parent_educ +
lunch_type + test_prep + parent_marital_status + practice_sport +
is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
lunch_type:practice_sport + lunch_type:wkly_study_hours +
parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)
library('MASS')##
## Attaching package: 'MASS'## The following object is masked from 'package:gtsummary':
##
## select## The following object is masked from 'package:dplyr':
##
## selectboxcox(step_as_lm_write)
step_as_lm_write=lm(formula = (writing_score)^2 ~ gender + ethnic_group + parent_educ +
lunch_type + test_prep + parent_marital_status + practice_sport +
is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
lunch_type:practice_sport + lunch_type:wkly_study_hours +
parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours, data = df_4_mdl_write)
plot(step_as_lm_write)
plot(stepwise_model_math)## Warning: not plotting observations with leverage one:
## 190
step_as_lm_math=lm(formula = math_score ~ gender + ethnic_group + parent_educ +
lunch_type + test_prep + parent_marital_status + practice_sport +
is_first_child + transport_means + wkly_study_hours + ethnic_group:transport_means +
parent_educ:parent_marital_status + parent_educ:is_first_child +
lunch_type:practice_sport + lunch_type:transport_means +
test_prep:is_first_child + test_prep:wkly_study_hours + parent_marital_status:is_first_child +
parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
is_first_child:transport_means + is_first_child:wkly_study_hours,data = df_4_mdl_math)plot(stepwise_model_read)
##ADD in other scores
Writing Score2
df_4_mdl_write2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,writing_score,math_score,reading_score)
full_fit_write2=lm(writing_score ~ .^2,data=df_4_mdl_write2)summary(full_fit_write2)##
## Call:
## lm(formula = writing_score ~ .^2, data = df_4_mdl_write2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.997 -1.687 0.000 1.784 7.682
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error
## (Intercept) 1.028e+01 8.576e+00
## gendermale -7.013e+00 3.989e+00
## ethnic_groupgroup B 3.669e-01 6.023e+00
## ethnic_groupgroup C -3.800e+00 5.577e+00
## ethnic_groupgroup D 3.108e+00 5.859e+00
## ethnic_groupgroup E 3.619e+00 5.900e+00
## parent_educbachelor's degree -2.540e+00 5.912e+00
## parent_educhigh school 7.053e-01 4.353e+00
## parent_educmaster's degree 1.423e+01 6.930e+00
## parent_educsome college -3.972e+00 4.298e+00
## parent_educsome high school 9.619e-01 4.179e+00
## lunch_typestandard 1.690e+00 3.496e+00
## test_prepnone -3.741e+00 3.414e+00
## parent_marital_statusmarried 7.848e+00 4.378e+00
## parent_marital_statussingle 9.743e+00 5.012e+00
## parent_marital_statuswidowed 2.301e+00 1.116e+01
## practice_sportregularly -6.078e+00 5.488e+00
## practice_sportsometimes -8.824e+00 5.349e+00
## is_first_childyes -1.382e+00 3.323e+00
## transport_meansschool_bus -6.443e+00 3.169e+00
## wkly_study_hours> 10 1.226e+00 4.722e+00
## wkly_study_hours10-May -2.133e+00 3.735e+00
## math_score 2.128e-01 2.386e-01
## reading_score 7.610e-01 2.255e-01
## gendermale:ethnic_groupgroup B -4.528e+00 2.318e+00
## gendermale:ethnic_groupgroup C -3.411e+00 2.215e+00
## gendermale:ethnic_groupgroup D -2.747e+00 2.176e+00
## gendermale:ethnic_groupgroup E -4.336e+00 2.470e+00
## gendermale:parent_educbachelor's degree 1.915e+00 1.709e+00
## gendermale:parent_educhigh school 8.177e-01 1.419e+00
## gendermale:parent_educmaster's degree -1.360e-01 3.810e+00
## gendermale:parent_educsome college 1.738e-01 1.488e+00
## gendermale:parent_educsome high school -3.763e-01 1.495e+00
## gendermale:lunch_typestandard -1.093e-01 1.143e+00
## gendermale:test_prepnone 3.385e-01 1.108e+00
## gendermale:parent_marital_statusmarried -2.482e-01 1.519e+00
## gendermale:parent_marital_statussingle 1.505e+00 1.728e+00
## gendermale:parent_marital_statuswidowed 4.344e-01 4.909e+00
## gendermale:practice_sportregularly 5.286e-01 2.043e+00
## gendermale:practice_sportsometimes 3.329e-01 1.971e+00
## gendermale:is_first_childyes 1.137e+00 1.132e+00
## gendermale:transport_meansschool_bus 3.868e-01 1.002e+00
## gendermale:wkly_study_hours> 10 -1.949e+00 1.673e+00
## gendermale:wkly_study_hours10-May -9.213e-01 1.184e+00
## gendermale:math_score -4.901e-02 5.875e-02
## gendermale:reading_score 8.724e-02 6.041e-02
## ethnic_groupgroup B:parent_educbachelor's degree -2.360e+00 3.631e+00
## ethnic_groupgroup C:parent_educbachelor's degree -3.922e+00 3.587e+00
## ethnic_groupgroup D:parent_educbachelor's degree -4.107e+00 3.539e+00
## ethnic_groupgroup E:parent_educbachelor's degree -2.158e+00 4.239e+00
## ethnic_groupgroup B:parent_educhigh school -2.294e+00 2.179e+00
## ethnic_groupgroup C:parent_educhigh school -2.333e+00 2.069e+00
## ethnic_groupgroup D:parent_educhigh school -1.623e+00 2.103e+00
## ethnic_groupgroup E:parent_educhigh school -3.068e+00 2.385e+00
## ethnic_groupgroup B:parent_educmaster's degree -1.163e+01 4.440e+00
## ethnic_groupgroup C:parent_educmaster's degree -1.099e+01 3.994e+00
## ethnic_groupgroup D:parent_educmaster's degree -8.580e+00 4.058e+00
## ethnic_groupgroup E:parent_educmaster's degree -8.886e+00 4.384e+00
## ethnic_groupgroup B:parent_educsome college -1.154e+00 2.454e+00
## ethnic_groupgroup C:parent_educsome college -8.806e-01 2.278e+00
## ethnic_groupgroup D:parent_educsome college -2.386e+00 2.390e+00
## ethnic_groupgroup E:parent_educsome college -4.769e+00 2.430e+00
## ethnic_groupgroup B:parent_educsome high school -4.318e+00 2.358e+00
## ethnic_groupgroup C:parent_educsome high school -4.749e+00 2.163e+00
## ethnic_groupgroup D:parent_educsome high school -3.744e+00 2.166e+00
## ethnic_groupgroup E:parent_educsome high school -7.797e+00 2.355e+00
## ethnic_groupgroup B:lunch_typestandard -4.576e+00 1.727e+00
## ethnic_groupgroup C:lunch_typestandard -4.132e+00 1.672e+00
## ethnic_groupgroup D:lunch_typestandard -5.504e+00 1.637e+00
## ethnic_groupgroup E:lunch_typestandard -3.755e+00 1.976e+00
## ethnic_groupgroup B:test_prepnone 7.983e-02 1.730e+00
## ethnic_groupgroup C:test_prepnone -8.576e-01 1.616e+00
## ethnic_groupgroup D:test_prepnone -1.329e+00 1.612e+00
## ethnic_groupgroup E:test_prepnone -6.585e-01 1.755e+00
## ethnic_groupgroup B:parent_marital_statusmarried -4.694e+00 2.252e+00
## ethnic_groupgroup C:parent_marital_statusmarried -3.813e+00 1.992e+00
## ethnic_groupgroup D:parent_marital_statusmarried -3.013e+00 1.991e+00
## ethnic_groupgroup E:parent_marital_statusmarried -4.379e+00 2.264e+00
## ethnic_groupgroup B:parent_marital_statussingle -6.236e+00 2.612e+00
## ethnic_groupgroup C:parent_marital_statussingle -4.982e+00 2.421e+00
## ethnic_groupgroup D:parent_marital_statussingle -4.474e+00 2.384e+00
## ethnic_groupgroup E:parent_marital_statussingle -8.456e+00 2.778e+00
## ethnic_groupgroup B:parent_marital_statuswidowed 4.573e+00 2.910e+01
## ethnic_groupgroup C:parent_marital_statuswidowed 1.408e+01 2.461e+01
## ethnic_groupgroup D:parent_marital_statuswidowed 6.284e-01 2.303e+01
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 2.264e+00 2.949e+00
## ethnic_groupgroup C:practice_sportregularly 4.746e+00 2.905e+00
## ethnic_groupgroup D:practice_sportregularly 1.567e+00 3.190e+00
## ethnic_groupgroup E:practice_sportregularly -1.058e+00 3.052e+00
## ethnic_groupgroup B:practice_sportsometimes 2.424e+00 3.132e+00
## ethnic_groupgroup C:practice_sportsometimes 4.488e+00 3.023e+00
## ethnic_groupgroup D:practice_sportsometimes 2.401e+00 3.280e+00
## ethnic_groupgroup E:practice_sportsometimes 1.404e+00 3.099e+00
## ethnic_groupgroup B:is_first_childyes 2.061e+00 1.583e+00
## ethnic_groupgroup C:is_first_childyes 3.185e+00 1.484e+00
## ethnic_groupgroup D:is_first_childyes 2.468e+00 1.515e+00
## ethnic_groupgroup E:is_first_childyes 3.012e+00 1.753e+00
## ethnic_groupgroup B:transport_meansschool_bus -1.396e-01 1.638e+00
## ethnic_groupgroup C:transport_meansschool_bus -7.759e-02 1.498e+00
## ethnic_groupgroup D:transport_meansschool_bus -1.696e+00 1.497e+00
## ethnic_groupgroup E:transport_meansschool_bus -1.491e+00 1.825e+00
## ethnic_groupgroup B:wkly_study_hours> 10 5.802e-01 2.726e+00
## ethnic_groupgroup C:wkly_study_hours> 10 1.954e-01 2.722e+00
## ethnic_groupgroup D:wkly_study_hours> 10 3.977e+00 2.734e+00
## ethnic_groupgroup E:wkly_study_hours> 10 1.303e+00 2.947e+00
## ethnic_groupgroup B:wkly_study_hours10-May -2.546e-01 2.236e+00
## ethnic_groupgroup C:wkly_study_hours10-May 1.636e+00 2.192e+00
## ethnic_groupgroup D:wkly_study_hours10-May 2.822e+00 2.233e+00
## ethnic_groupgroup E:wkly_study_hours10-May 3.406e+00 2.445e+00
## ethnic_groupgroup B:math_score 3.236e-01 1.452e-01
## ethnic_groupgroup C:math_score 2.304e-01 1.365e-01
## ethnic_groupgroup D:math_score 2.338e-01 1.351e-01
## ethnic_groupgroup E:math_score 2.302e-01 1.600e-01
## ethnic_groupgroup B:reading_score -1.914e-01 1.362e-01
## ethnic_groupgroup C:reading_score -1.056e-01 1.296e-01
## ethnic_groupgroup D:reading_score -1.470e-01 1.272e-01
## ethnic_groupgroup E:reading_score -1.390e-01 1.506e-01
## parent_educbachelor's degree:lunch_typestandard 9.535e-01 1.525e+00
## parent_educhigh school:lunch_typestandard 9.227e-01 1.205e+00
## parent_educmaster's degree:lunch_typestandard -8.538e-01 3.193e+00
## parent_educsome college:lunch_typestandard 2.284e+00 1.225e+00
## parent_educsome high school:lunch_typestandard -1.360e-01 1.292e+00
## parent_educbachelor's degree:test_prepnone 1.560e+00 1.290e+00
## parent_educhigh school:test_prepnone 9.003e-01 1.230e+00
## parent_educmaster's degree:test_prepnone -3.015e+00 2.150e+00
## parent_educsome college:test_prepnone 1.179e+00 1.144e+00
## parent_educsome high school:test_prepnone -5.264e-02 1.115e+00
## parent_educbachelor's degree:parent_marital_statusmarried -8.048e-01 2.433e+00
## parent_educhigh school:parent_marital_statusmarried -1.460e+00 1.679e+00
## parent_educmaster's degree:parent_marital_statusmarried 4.700e+00 2.454e+00
## parent_educsome college:parent_marital_statusmarried 1.767e+00 1.575e+00
## parent_educsome high school:parent_marital_statusmarried 9.859e-01 1.551e+00
## parent_educbachelor's degree:parent_marital_statussingle -1.603e+00 2.721e+00
## parent_educhigh school:parent_marital_statussingle -1.213e-02 1.797e+00
## parent_educmaster's degree:parent_marital_statussingle 2.822e+00 2.512e+00
## parent_educsome college:parent_marital_statussingle 1.659e+00 1.731e+00
## parent_educsome high school:parent_marital_statussingle -4.275e-01 1.752e+00
## parent_educbachelor's degree:parent_marital_statuswidowed 5.047e+00 2.313e+01
## parent_educhigh school:parent_marital_statuswidowed 2.332e+00 2.647e+01
## parent_educmaster's degree:parent_marital_statuswidowed -7.201e+00 1.459e+01
## parent_educsome college:parent_marital_statuswidowed -8.571e+00 1.816e+01
## parent_educsome high school:parent_marital_statuswidowed -5.909e+00 2.125e+01
## parent_educbachelor's degree:practice_sportregularly 5.133e+00 2.376e+00
## parent_educhigh school:practice_sportregularly 2.626e+00 1.959e+00
## parent_educmaster's degree:practice_sportregularly 5.789e-01 2.823e+00
## parent_educsome college:practice_sportregularly 5.130e-01 1.989e+00
## parent_educsome high school:practice_sportregularly 4.815e-01 1.910e+00
## parent_educbachelor's degree:practice_sportsometimes 3.054e+00 2.271e+00
## parent_educhigh school:practice_sportsometimes 1.137e+00 1.884e+00
## parent_educmaster's degree:practice_sportsometimes -6.126e-01 2.565e+00
## parent_educsome college:practice_sportsometimes 1.530e+00 1.958e+00
## parent_educsome high school:practice_sportsometimes -2.079e+00 1.792e+00
## parent_educbachelor's degree:is_first_childyes 2.548e+00 1.357e+00
## parent_educhigh school:is_first_childyes 9.976e-01 1.182e+00
## parent_educmaster's degree:is_first_childyes -3.160e+00 2.129e+00
## parent_educsome college:is_first_childyes 2.851e+00 1.161e+00
## parent_educsome high school:is_first_childyes 2.358e+00 1.164e+00
## parent_educbachelor's degree:transport_meansschool_bus 4.026e-01 1.388e+00
## parent_educhigh school:transport_meansschool_bus 7.477e-01 1.102e+00
## parent_educmaster's degree:transport_meansschool_bus 6.615e-01 1.827e+00
## parent_educsome college:transport_meansschool_bus -8.132e-01 1.128e+00
## parent_educsome high school:transport_meansschool_bus 1.680e+00 1.166e+00
## parent_educbachelor's degree:wkly_study_hours> 10 -1.506e-01 2.039e+00
## parent_educhigh school:wkly_study_hours> 10 -2.687e-01 1.679e+00
## parent_educmaster's degree:wkly_study_hours> 10 -2.737e+00 4.402e+00
## parent_educsome college:wkly_study_hours> 10 -2.302e+00 1.720e+00
## parent_educsome high school:wkly_study_hours> 10 -1.359e+00 1.743e+00
## parent_educbachelor's degree:wkly_study_hours10-May -7.253e-01 1.418e+00
## parent_educhigh school:wkly_study_hours10-May -1.045e+00 1.332e+00
## parent_educmaster's degree:wkly_study_hours10-May -2.224e+00 2.130e+00
## parent_educsome college:wkly_study_hours10-May -2.599e+00 1.353e+00
## parent_educsome high school:wkly_study_hours10-May -4.571e-01 1.421e+00
## parent_educbachelor's degree:math_score -1.932e-01 1.072e-01
## parent_educhigh school:math_score -7.404e-02 8.469e-02
## parent_educmaster's degree:math_score 1.057e-01 2.392e-01
## parent_educsome college:math_score 5.119e-03 8.827e-02
## parent_educsome high school:math_score -3.364e-02 8.807e-02
## parent_educbachelor's degree:reading_score 1.891e-01 1.148e-01
## parent_educhigh school:reading_score 3.758e-02 8.697e-02
## parent_educmaster's degree:reading_score -9.233e-02 2.097e-01
## parent_educsome college:reading_score 2.167e-02 9.021e-02
## parent_educsome high school:reading_score 3.768e-02 8.729e-02
## lunch_typestandard:test_prepnone 2.260e-01 9.141e-01
## lunch_typestandard:parent_marital_statusmarried -3.873e-01 1.196e+00
## lunch_typestandard:parent_marital_statussingle -1.706e+00 1.393e+00
## lunch_typestandard:parent_marital_statuswidowed 1.749e+00 2.137e+01
## lunch_typestandard:practice_sportregularly 6.608e-01 1.503e+00
## lunch_typestandard:practice_sportsometimes 1.637e+00 1.411e+00
## lunch_typestandard:is_first_childyes -9.874e-01 9.280e-01
## lunch_typestandard:transport_meansschool_bus -1.920e-01 8.672e-01
## lunch_typestandard:wkly_study_hours> 10 -3.781e-01 1.331e+00
## lunch_typestandard:wkly_study_hours10-May 3.552e-01 1.014e+00
## lunch_typestandard:math_score 3.561e-02 6.063e-02
## lunch_typestandard:reading_score -4.639e-03 6.218e-02
## test_prepnone:parent_marital_statusmarried -3.030e+00 1.151e+00
## test_prepnone:parent_marital_statussingle -2.900e+00 1.329e+00
## test_prepnone:parent_marital_statuswidowed -8.578e+00 1.207e+01
## test_prepnone:practice_sportregularly 3.008e-01 1.444e+00
## test_prepnone:practice_sportsometimes 1.806e+00 1.406e+00
## test_prepnone:is_first_childyes -9.820e-01 8.431e-01
## test_prepnone:transport_meansschool_bus 1.484e+00 7.799e-01
## test_prepnone:wkly_study_hours> 10 1.023e-01 1.199e+00
## test_prepnone:wkly_study_hours10-May 5.061e-01 9.656e-01
## test_prepnone:math_score -8.815e-03 6.136e-02
## test_prepnone:reading_score 2.202e-02 6.343e-02
## parent_marital_statusmarried:practice_sportregularly -1.129e+00 1.761e+00
## parent_marital_statussingle:practice_sportregularly -2.999e+00 2.393e+00
## parent_marital_statuswidowed:practice_sportregularly -6.007e+00 2.241e+01
## parent_marital_statusmarried:practice_sportsometimes -3.916e-01 1.754e+00
## parent_marital_statussingle:practice_sportsometimes -2.731e+00 2.338e+00
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -4.629e-01 1.419e+00
## parent_marital_statussingle:is_first_childyes -4.861e-01 1.526e+00
## parent_marital_statuswidowed:is_first_childyes 6.577e+00 8.406e+00
## parent_marital_statusmarried:transport_meansschool_bus -4.278e-01 1.115e+00
## parent_marital_statussingle:transport_meansschool_bus 9.514e-01 1.272e+00
## parent_marital_statuswidowed:transport_meansschool_bus -2.336e+00 5.656e+00
## parent_marital_statusmarried:wkly_study_hours> 10 1.170e-01 1.870e+00
## parent_marital_statussingle:wkly_study_hours> 10 1.130e+00 2.047e+00
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 2.756e+00 1.205e+00
## parent_marital_statussingle:wkly_study_hours10-May 3.963e+00 1.348e+00
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:math_score 2.480e-02 9.188e-02
## parent_marital_statussingle:math_score -7.269e-02 1.017e-01
## parent_marital_statuswidowed:math_score NA NA
## parent_marital_statusmarried:reading_score -6.129e-02 9.651e-02
## parent_marital_statussingle:reading_score 3.787e-02 1.069e-01
## parent_marital_statuswidowed:reading_score NA NA
## practice_sportregularly:is_first_childyes -2.264e+00 1.585e+00
## practice_sportsometimes:is_first_childyes -1.184e+00 1.538e+00
## practice_sportregularly:transport_meansschool_bus 1.020e+00 1.371e+00
## practice_sportsometimes:transport_meansschool_bus 7.856e-01 1.330e+00
## practice_sportregularly:wkly_study_hours> 10 1.816e+00 1.893e+00
## practice_sportsometimes:wkly_study_hours> 10 3.907e-01 1.870e+00
## practice_sportregularly:wkly_study_hours10-May -4.035e-02 1.453e+00
## practice_sportsometimes:wkly_study_hours10-May -8.301e-01 1.430e+00
## practice_sportregularly:math_score 4.761e-02 1.358e-01
## practice_sportsometimes:math_score 7.168e-03 1.328e-01
## practice_sportregularly:reading_score 2.189e-02 1.325e-01
## practice_sportsometimes:reading_score 6.724e-02 1.290e-01
## is_first_childyes:transport_meansschool_bus -4.867e-01 8.253e-01
## is_first_childyes:wkly_study_hours> 10 1.378e+00 1.219e+00
## is_first_childyes:wkly_study_hours10-May 1.474e+00 9.252e-01
## is_first_childyes:math_score -6.407e-02 6.526e-02
## is_first_childyes:reading_score 4.464e-02 6.619e-02
## transport_meansschool_bus:wkly_study_hours> 10 -7.931e-02 1.197e+00
## transport_meansschool_bus:wkly_study_hours10-May -8.356e-01 8.378e-01
## transport_meansschool_bus:math_score 3.887e-02 6.030e-02
## transport_meansschool_bus:reading_score 4.383e-02 6.201e-02
## wkly_study_hours> 10:math_score 1.049e-01 9.306e-02
## wkly_study_hours10-May:math_score -1.912e-03 6.687e-02
## wkly_study_hours> 10:reading_score -1.469e-01 9.748e-02
## wkly_study_hours10-May:reading_score -1.354e-02 6.492e-02
## math_score:reading_score -1.711e-03 8.452e-04
## t value Pr(>|t|)
## (Intercept) 1.199 0.231456
## gendermale -1.758 0.079623 .
## ethnic_groupgroup B 0.061 0.951460
## ethnic_groupgroup C -0.681 0.496075
## ethnic_groupgroup D 0.530 0.596167
## ethnic_groupgroup E 0.613 0.539968
## parent_educbachelor's degree -0.430 0.667787
## parent_educhigh school 0.162 0.871389
## parent_educmaster's degree 2.053 0.040810 *
## parent_educsome college -0.924 0.356042
## parent_educsome high school 0.230 0.818085
## lunch_typestandard 0.483 0.629192
## test_prepnone -1.096 0.273983
## parent_marital_statusmarried 1.793 0.073914 .
## parent_marital_statussingle 1.944 0.052719 .
## parent_marital_statuswidowed 0.206 0.836786
## practice_sportregularly -1.108 0.268841
## practice_sportsometimes -1.650 0.099912 .
## is_first_childyes -0.416 0.677621
## transport_meansschool_bus -2.033 0.042785 *
## wkly_study_hours> 10 0.260 0.795349
## wkly_study_hours10-May -0.571 0.568305
## math_score 0.892 0.373099
## reading_score 3.375 0.000824 ***
## gendermale:ethnic_groupgroup B -1.954 0.051551 .
## gendermale:ethnic_groupgroup C -1.540 0.124591
## gendermale:ethnic_groupgroup D -1.262 0.207727
## gendermale:ethnic_groupgroup E -1.756 0.080050 .
## gendermale:parent_educbachelor's degree 1.121 0.263118
## gendermale:parent_educhigh school 0.576 0.564776
## gendermale:parent_educmaster's degree -0.036 0.971534
## gendermale:parent_educsome college 0.117 0.907096
## gendermale:parent_educsome high school -0.252 0.801470
## gendermale:lunch_typestandard -0.096 0.923917
## gendermale:test_prepnone 0.306 0.760096
## gendermale:parent_marital_statusmarried -0.163 0.870316
## gendermale:parent_marital_statussingle 0.871 0.384205
## gendermale:parent_marital_statuswidowed 0.088 0.929540
## gendermale:practice_sportregularly 0.259 0.796023
## gendermale:practice_sportsometimes 0.169 0.865950
## gendermale:is_first_childyes 1.004 0.315869
## gendermale:transport_meansschool_bus 0.386 0.699760
## gendermale:wkly_study_hours> 10 -1.165 0.244954
## gendermale:wkly_study_hours10-May -0.778 0.437068
## gendermale:math_score -0.834 0.404755
## gendermale:reading_score 1.444 0.149600
## ethnic_groupgroup B:parent_educbachelor's degree -0.650 0.516141
## ethnic_groupgroup C:parent_educbachelor's degree -1.094 0.274921
## ethnic_groupgroup D:parent_educbachelor's degree -1.160 0.246726
## ethnic_groupgroup E:parent_educbachelor's degree -0.509 0.610969
## ethnic_groupgroup B:parent_educhigh school -1.053 0.293150
## ethnic_groupgroup C:parent_educhigh school -1.128 0.260320
## ethnic_groupgroup D:parent_educhigh school -0.772 0.440647
## ethnic_groupgroup E:parent_educhigh school -1.286 0.199283
## ethnic_groupgroup B:parent_educmaster's degree -2.619 0.009201 **
## ethnic_groupgroup C:parent_educmaster's degree -2.750 0.006274 **
## ethnic_groupgroup D:parent_educmaster's degree -2.114 0.035211 *
## ethnic_groupgroup E:parent_educmaster's degree -2.027 0.043436 *
## ethnic_groupgroup B:parent_educsome college -0.470 0.638494
## ethnic_groupgroup C:parent_educsome college -0.387 0.699356
## ethnic_groupgroup D:parent_educsome college -0.998 0.318802
## ethnic_groupgroup E:parent_educsome college -1.962 0.050544 .
## ethnic_groupgroup B:parent_educsome high school -1.831 0.067918 .
## ethnic_groupgroup C:parent_educsome high school -2.195 0.028833 *
## ethnic_groupgroup D:parent_educsome high school -1.729 0.084730 .
## ethnic_groupgroup E:parent_educsome high school -3.311 0.001031 **
## ethnic_groupgroup B:lunch_typestandard -2.650 0.008431 **
## ethnic_groupgroup C:lunch_typestandard -2.471 0.013973 *
## ethnic_groupgroup D:lunch_typestandard -3.362 0.000863 ***
## ethnic_groupgroup E:lunch_typestandard -1.901 0.058203 .
## ethnic_groupgroup B:test_prepnone 0.046 0.963213
## ethnic_groupgroup C:test_prepnone -0.531 0.596082
## ethnic_groupgroup D:test_prepnone -0.825 0.410230
## ethnic_groupgroup E:test_prepnone -0.375 0.707810
## ethnic_groupgroup B:parent_marital_statusmarried -2.085 0.037859 *
## ethnic_groupgroup C:parent_marital_statusmarried -1.915 0.056384 .
## ethnic_groupgroup D:parent_marital_statusmarried -1.513 0.131123
## ethnic_groupgroup E:parent_marital_statusmarried -1.935 0.053869 .
## ethnic_groupgroup B:parent_marital_statussingle -2.388 0.017499 *
## ethnic_groupgroup C:parent_marital_statussingle -2.058 0.040375 *
## ethnic_groupgroup D:parent_marital_statussingle -1.876 0.061480 .
## ethnic_groupgroup E:parent_marital_statussingle -3.044 0.002519 **
## ethnic_groupgroup B:parent_marital_statuswidowed 0.157 0.875232
## ethnic_groupgroup C:parent_marital_statuswidowed 0.572 0.567578
## ethnic_groupgroup D:parent_marital_statuswidowed 0.027 0.978245
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 0.768 0.443133
## ethnic_groupgroup C:practice_sportregularly 1.634 0.103284
## ethnic_groupgroup D:practice_sportregularly 0.491 0.623729
## ethnic_groupgroup E:practice_sportregularly -0.347 0.729127
## ethnic_groupgroup B:practice_sportsometimes 0.774 0.439531
## ethnic_groupgroup C:practice_sportsometimes 1.484 0.138643
## ethnic_groupgroup D:practice_sportsometimes 0.732 0.464661
## ethnic_groupgroup E:practice_sportsometimes 0.453 0.650804
## ethnic_groupgroup B:is_first_childyes 1.302 0.193881
## ethnic_groupgroup C:is_first_childyes 2.146 0.032597 *
## ethnic_groupgroup D:is_first_childyes 1.630 0.104116
## ethnic_groupgroup E:is_first_childyes 1.718 0.086624 .
## ethnic_groupgroup B:transport_meansschool_bus -0.085 0.932158
## ethnic_groupgroup C:transport_meansschool_bus -0.052 0.958719
## ethnic_groupgroup D:transport_meansschool_bus -1.133 0.258165
## ethnic_groupgroup E:transport_meansschool_bus -0.817 0.414538
## ethnic_groupgroup B:wkly_study_hours> 10 0.213 0.831564
## ethnic_groupgroup C:wkly_study_hours> 10 0.072 0.942813
## ethnic_groupgroup D:wkly_study_hours> 10 1.454 0.146733
## ethnic_groupgroup E:wkly_study_hours> 10 0.442 0.658552
## ethnic_groupgroup B:wkly_study_hours10-May -0.114 0.909384
## ethnic_groupgroup C:wkly_study_hours10-May 0.746 0.456140
## ethnic_groupgroup D:wkly_study_hours10-May 1.264 0.207115
## ethnic_groupgroup E:wkly_study_hours10-May 1.393 0.164584
## ethnic_groupgroup B:math_score 2.228 0.026504 *
## ethnic_groupgroup C:math_score 1.688 0.092282 .
## ethnic_groupgroup D:math_score 1.730 0.084453 .
## ethnic_groupgroup E:math_score 1.439 0.151200
## ethnic_groupgroup B:reading_score -1.406 0.160652
## ethnic_groupgroup C:reading_score -0.815 0.415690
## ethnic_groupgroup D:reading_score -1.156 0.248457
## ethnic_groupgroup E:reading_score -0.922 0.356937
## parent_educbachelor's degree:lunch_typestandard 0.625 0.532190
## parent_educhigh school:lunch_typestandard 0.766 0.444428
## parent_educmaster's degree:lunch_typestandard -0.267 0.789339
## parent_educsome college:lunch_typestandard 1.864 0.063177 .
## parent_educsome high school:lunch_typestandard -0.105 0.916212
## parent_educbachelor's degree:test_prepnone 1.209 0.227508
## parent_educhigh school:test_prepnone 0.732 0.464686
## parent_educmaster's degree:test_prepnone -1.402 0.161767
## parent_educsome college:test_prepnone 1.030 0.303562
## parent_educsome high school:test_prepnone -0.047 0.962354
## parent_educbachelor's degree:parent_marital_statusmarried -0.331 0.741044
## parent_educhigh school:parent_marital_statusmarried -0.870 0.385073
## parent_educmaster's degree:parent_marital_statusmarried 1.915 0.056296 .
## parent_educsome college:parent_marital_statusmarried 1.122 0.262607
## parent_educsome high school:parent_marital_statusmarried 0.636 0.525383
## parent_educbachelor's degree:parent_marital_statussingle -0.589 0.556280
## parent_educhigh school:parent_marital_statussingle -0.007 0.994617
## parent_educmaster's degree:parent_marital_statussingle 1.123 0.262066
## parent_educsome college:parent_marital_statussingle 0.959 0.338359
## parent_educsome high school:parent_marital_statussingle -0.244 0.807365
## parent_educbachelor's degree:parent_marital_statuswidowed 0.218 0.827400
## parent_educhigh school:parent_marital_statuswidowed 0.088 0.929870
## parent_educmaster's degree:parent_marital_statuswidowed -0.494 0.621922
## parent_educsome college:parent_marital_statuswidowed -0.472 0.637175
## parent_educsome high school:parent_marital_statuswidowed -0.278 0.781139
## parent_educbachelor's degree:practice_sportregularly 2.160 0.031468 *
## parent_educhigh school:practice_sportregularly 1.340 0.181144
## parent_educmaster's degree:practice_sportregularly 0.205 0.837663
## parent_educsome college:practice_sportregularly 0.258 0.796631
## parent_educsome high school:practice_sportregularly 0.252 0.801173
## parent_educbachelor's degree:practice_sportsometimes 1.345 0.179574
## parent_educhigh school:practice_sportsometimes 0.604 0.546457
## parent_educmaster's degree:practice_sportsometimes -0.239 0.811354
## parent_educsome college:practice_sportsometimes 0.782 0.434969
## parent_educsome high school:practice_sportsometimes -1.160 0.246687
## parent_educbachelor's degree:is_first_childyes 1.878 0.061283 .
## parent_educhigh school:is_first_childyes 0.844 0.399328
## parent_educmaster's degree:is_first_childyes -1.484 0.138693
## parent_educsome college:is_first_childyes 2.456 0.014533 *
## parent_educsome high school:is_first_childyes 2.026 0.043506 *
## parent_educbachelor's degree:transport_meansschool_bus 0.290 0.771982
## parent_educhigh school:transport_meansschool_bus 0.678 0.497920
## parent_educmaster's degree:transport_meansschool_bus 0.362 0.717468
## parent_educsome college:transport_meansschool_bus -0.721 0.471520
## parent_educsome high school:transport_meansschool_bus 1.441 0.150635
## parent_educbachelor's degree:wkly_study_hours> 10 -0.074 0.941138
## parent_educhigh school:wkly_study_hours> 10 -0.160 0.872940
## parent_educmaster's degree:wkly_study_hours> 10 -0.622 0.534578
## parent_educsome college:wkly_study_hours> 10 -1.338 0.181799
## parent_educsome high school:wkly_study_hours> 10 -0.780 0.435922
## parent_educbachelor's degree:wkly_study_hours10-May -0.511 0.609403
## parent_educhigh school:wkly_study_hours10-May -0.785 0.433272
## parent_educmaster's degree:wkly_study_hours10-May -1.044 0.297081
## parent_educsome college:wkly_study_hours10-May -1.920 0.055680 .
## parent_educsome high school:wkly_study_hours10-May -0.322 0.747860
## parent_educbachelor's degree:math_score -1.802 0.072457 .
## parent_educhigh school:math_score -0.874 0.382598
## parent_educmaster's degree:math_score 0.442 0.658912
## parent_educsome college:math_score 0.058 0.953783
## parent_educsome high school:math_score -0.382 0.702748
## parent_educbachelor's degree:reading_score 1.648 0.100376
## parent_educhigh school:reading_score 0.432 0.665928
## parent_educmaster's degree:reading_score -0.440 0.659957
## parent_educsome college:reading_score 0.240 0.810322
## parent_educsome high school:reading_score 0.432 0.666207
## lunch_typestandard:test_prepnone 0.247 0.804865
## lunch_typestandard:parent_marital_statusmarried -0.324 0.746205
## lunch_typestandard:parent_marital_statussingle -1.224 0.221656
## lunch_typestandard:parent_marital_statuswidowed 0.082 0.934829
## lunch_typestandard:practice_sportregularly 0.440 0.660361
## lunch_typestandard:practice_sportsometimes 1.160 0.246956
## lunch_typestandard:is_first_childyes -1.064 0.288093
## lunch_typestandard:transport_meansschool_bus -0.221 0.824926
## lunch_typestandard:wkly_study_hours> 10 -0.284 0.776475
## lunch_typestandard:wkly_study_hours10-May 0.350 0.726219
## lunch_typestandard:math_score 0.587 0.557320
## lunch_typestandard:reading_score -0.075 0.940565
## test_prepnone:parent_marital_statusmarried -2.633 0.008849 **
## test_prepnone:parent_marital_statussingle -2.183 0.029715 *
## test_prepnone:parent_marital_statuswidowed -0.711 0.477729
## test_prepnone:practice_sportregularly 0.208 0.835044
## test_prepnone:practice_sportsometimes 1.284 0.199991
## test_prepnone:is_first_childyes -1.165 0.244915
## test_prepnone:transport_meansschool_bus 1.903 0.057941 .
## test_prepnone:wkly_study_hours> 10 0.085 0.932085
## test_prepnone:wkly_study_hours10-May 0.524 0.600519
## test_prepnone:math_score -0.144 0.885844
## test_prepnone:reading_score 0.347 0.728664
## parent_marital_statusmarried:practice_sportregularly -0.641 0.522028
## parent_marital_statussingle:practice_sportregularly -1.254 0.210869
## parent_marital_statuswidowed:practice_sportregularly -0.268 0.788808
## parent_marital_statusmarried:practice_sportsometimes -0.223 0.823464
## parent_marital_statussingle:practice_sportsometimes -1.168 0.243438
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -0.326 0.744549
## parent_marital_statussingle:is_first_childyes -0.319 0.750281
## parent_marital_statuswidowed:is_first_childyes 0.782 0.434517
## parent_marital_statusmarried:transport_meansschool_bus -0.384 0.701456
## parent_marital_statussingle:transport_meansschool_bus 0.748 0.455143
## parent_marital_statuswidowed:transport_meansschool_bus -0.413 0.679890
## parent_marital_statusmarried:wkly_study_hours> 10 0.063 0.950174
## parent_marital_statussingle:wkly_study_hours> 10 0.552 0.581417
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May 2.287 0.022780 *
## parent_marital_statussingle:wkly_study_hours10-May 2.941 0.003499 **
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:math_score 0.270 0.787397
## parent_marital_statussingle:math_score -0.715 0.475217
## parent_marital_statuswidowed:math_score NA NA
## parent_marital_statusmarried:reading_score -0.635 0.525774
## parent_marital_statussingle:reading_score 0.354 0.723458
## parent_marital_statuswidowed:reading_score NA NA
## practice_sportregularly:is_first_childyes -1.428 0.154105
## practice_sportsometimes:is_first_childyes -0.770 0.441802
## practice_sportregularly:transport_meansschool_bus 0.744 0.457620
## practice_sportsometimes:transport_meansschool_bus 0.591 0.554975
## practice_sportregularly:wkly_study_hours> 10 0.959 0.338040
## practice_sportsometimes:wkly_study_hours> 10 0.209 0.834632
## practice_sportregularly:wkly_study_hours10-May -0.028 0.977863
## practice_sportsometimes:wkly_study_hours10-May -0.580 0.561972
## practice_sportregularly:math_score 0.351 0.726157
## practice_sportsometimes:math_score 0.054 0.956995
## practice_sportregularly:reading_score 0.165 0.868917
## practice_sportsometimes:reading_score 0.521 0.602453
## is_first_childyes:transport_meansschool_bus -0.590 0.555756
## is_first_childyes:wkly_study_hours> 10 1.131 0.258956
## is_first_childyes:wkly_study_hours10-May 1.593 0.111981
## is_first_childyes:math_score -0.982 0.326904
## is_first_childyes:reading_score 0.674 0.500566
## transport_meansschool_bus:wkly_study_hours> 10 -0.066 0.947202
## transport_meansschool_bus:wkly_study_hours10-May -0.997 0.319290
## transport_meansschool_bus:math_score 0.645 0.519614
## transport_meansschool_bus:reading_score 0.707 0.480179
## wkly_study_hours> 10:math_score 1.127 0.260666
## wkly_study_hours10-May:math_score -0.029 0.977206
## wkly_study_hours> 10:reading_score -1.507 0.132714
## wkly_study_hours10-May:reading_score -0.209 0.834897
## math_score:reading_score -2.024 0.043746 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.297 on 340 degrees of freedom
## Multiple R-squared: 0.974, Adjusted R-squared: 0.9549
## F-statistic: 51.12 on 249 and 340 DF, p-value: < 2.2e-16stepwise_model_write2 <- step(full_fit_write2, direction = "both", trace = 1)## Start: AIC=1582.41
## writing_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score)^2
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 62.949 3757.9 1572.4
## - gender:parent_educ 5 22.786 3717.7 1576.0
## - ethnic_group:test_prep 4 19.882 3714.8 1577.6
## - parent_educ:reading_score 5 34.925 3729.8 1578.0
## - practice_sport:wkly_study_hours 4 25.790 3720.7 1578.5
## - ethnic_group:reading_score 4 25.971 3720.9 1578.5
## - gender:practice_sport 2 0.852 3695.8 1578.5
## - parent_marital_status:is_first_child 2 1.250 3696.2 1578.6
## - parent_marital_status:practice_sport 4 26.525 3721.4 1578.6
## - test_prep:wkly_study_hours 2 3.799 3698.7 1579.0
## - lunch_type:wkly_study_hours 2 4.745 3699.7 1579.2
## - practice_sport:math_score 2 4.955 3699.9 1579.2
## - practice_sport:transport_means 2 6.023 3700.9 1579.4
## - practice_sport:reading_score 2 7.373 3702.3 1579.6
## - parent_educ:math_score 5 49.405 3744.3 1580.2
## - lunch_type:reading_score 1 0.061 3695.0 1580.4
## - gender:lunch_type 1 0.099 3695.0 1580.4
## - test_prep:math_score 1 0.224 3695.1 1580.4
## - lunch_type:transport_means 1 0.533 3695.5 1580.5
## - transport_means:wkly_study_hours 2 13.188 3708.1 1580.5
## - lunch_type:test_prep 1 0.664 3695.6 1580.5
## - gender:test_prep 1 1.015 3695.9 1580.6
## - parent_educ:lunch_type 5 51.531 3746.5 1580.6
## - test_prep:reading_score 1 1.310 3696.2 1580.6
## - gender:transport_means 1 1.619 3696.5 1580.7
## - gender:wkly_study_hours 2 15.457 3710.4 1580.9
## - parent_educ:transport_means 5 53.997 3748.9 1581.0
## - lunch_type:math_score 1 3.750 3698.7 1581.0
## - is_first_child:transport_means 1 3.780 3698.7 1581.0
## - ethnic_group:transport_means 4 41.700 3736.6 1581.0
## - transport_means:math_score 1 4.516 3699.4 1581.1
## - is_first_child:reading_score 1 4.941 3699.9 1581.2
## - transport_means:reading_score 1 5.429 3700.3 1581.3
## - wkly_study_hours:math_score 2 18.912 3713.8 1581.4
## - gender:math_score 1 7.562 3702.5 1581.6
## - lunch_type:practice_sport 2 21.534 3716.5 1581.8
## - parent_marital_status:math_score 2 22.471 3717.4 1582.0
## - parent_marital_status:reading_score 2 22.811 3717.7 1582.0
## - lunch_type:parent_marital_status 2 22.922 3717.8 1582.1
## - is_first_child:math_score 1 10.475 3705.4 1582.1
## - parent_marital_status:transport_means 2 23.343 3718.3 1582.1
## - gender:parent_marital_status 2 23.417 3718.3 1582.1
## - gender:is_first_child 1 10.965 3705.9 1582.2
## - lunch_type:is_first_child 1 12.302 3707.2 1582.4
## <none> 3694.9 1582.4
## - parent_educ:test_prep 5 63.715 3758.6 1582.5
## - gender:ethnic_group 4 51.066 3746.0 1582.5
## - test_prep:is_first_child 1 14.745 3709.7 1582.8
## - wkly_study_hours:reading_score 2 27.420 3722.3 1582.8
## - ethnic_group:is_first_child 4 53.175 3748.1 1582.8
## - is_first_child:wkly_study_hours 2 28.963 3723.9 1583.0
## - ethnic_group:math_score 4 55.062 3750.0 1583.1
## - parent_educ:parent_marital_status 11 145.213 3840.1 1583.2
## - ethnic_group:practice_sport 8 108.662 3803.6 1583.5
## - practice_sport:is_first_child 2 32.316 3727.2 1583.5
## - gender:reading_score 1 22.667 3717.6 1584.0
## - test_prep:practice_sport 2 46.200 3741.1 1585.7
## - ethnic_group:parent_marital_status 8 125.322 3820.2 1586.1
## - test_prep:transport_means 1 39.338 3734.3 1586.7
## - math_score:reading_score 1 44.522 3739.4 1587.5
## - ethnic_group:parent_educ 20 302.255 3997.2 1588.8
## - test_prep:parent_marital_status 2 76.280 3771.2 1590.5
## - parent_educ:practice_sport 10 187.276 3882.2 1591.6
## - parent_marital_status:wkly_study_hours 4 111.531 3806.5 1592.0
## - ethnic_group:wkly_study_hours 8 176.795 3871.7 1594.0
## - ethnic_group:lunch_type 4 125.572 3820.5 1594.1
## - parent_educ:is_first_child 5 151.702 3846.6 1596.2
##
## Step: AIC=1572.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:math_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + ethnic_group:reading_score + parent_educ:lunch_type +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 27.583 3785.5 1566.7
## - parent_educ:reading_score 5 31.853 3789.7 1567.4
## - ethnic_group:reading_score 4 22.722 3780.6 1567.9
## - practice_sport:wkly_study_hours 4 23.202 3781.1 1568.0
## - parent_marital_status:practice_sport 4 23.527 3781.4 1568.1
## - gender:practice_sport 2 0.743 3758.6 1568.5
## - parent_marital_status:is_first_child 2 1.305 3759.2 1568.6
## - test_prep:wkly_study_hours 2 1.619 3759.5 1568.6
## - ethnic_group:test_prep 4 28.611 3786.5 1568.8
## - practice_sport:transport_means 2 4.866 3762.7 1569.1
## - parent_educ:math_score 5 44.454 3802.3 1569.3
## - practice_sport:reading_score 2 6.715 3764.6 1569.4
## - lunch_type:wkly_study_hours 2 7.121 3765.0 1569.5
## - practice_sport:math_score 2 7.826 3765.7 1569.6
## - gender:wkly_study_hours 2 9.696 3767.6 1569.9
## - lunch_type:transport_means 1 0.019 3757.9 1570.4
## - test_prep:math_score 1 0.028 3757.9 1570.4
## - lunch_type:test_prep 1 0.093 3758.0 1570.4
## - lunch_type:reading_score 1 0.123 3758.0 1570.4
## - gender:lunch_type 1 0.239 3758.1 1570.4
## - gender:test_prep 1 0.286 3758.2 1570.4
## - test_prep:reading_score 1 0.641 3758.5 1570.5
## - ethnic_group:transport_means 4 39.439 3797.3 1570.5
## - gender:transport_means 1 2.277 3760.1 1570.7
## - transport_means:math_score 1 3.428 3761.3 1570.9
## - is_first_child:transport_means 1 3.540 3761.4 1570.9
## - parent_educ:transport_means 5 54.937 3812.8 1570.9
## - lunch_type:math_score 1 3.629 3761.5 1571.0
## - transport_means:wkly_study_hours 2 16.562 3774.4 1571.0
## - is_first_child:reading_score 1 5.275 3763.1 1571.2
## - wkly_study_hours:math_score 2 18.457 3776.3 1571.3
## - parent_marital_status:transport_means 2 19.317 3777.2 1571.4
## - transport_means:reading_score 1 6.841 3764.7 1571.5
## - lunch_type:practice_sport 2 19.837 3777.7 1571.5
## - gender:ethnic_group 4 46.794 3804.7 1571.7
## - parent_marital_status:math_score 2 21.227 3779.1 1571.7
## - is_first_child:wkly_study_hours 2 21.681 3779.6 1571.8
## - gender:math_score 1 9.244 3767.1 1571.8
## - gender:is_first_child 1 9.510 3767.4 1571.9
## - parent_marital_status:reading_score 2 22.326 3780.2 1571.9
## - lunch_type:parent_marital_status 2 22.805 3780.7 1572.0
## - ethnic_group:is_first_child 4 48.874 3806.7 1572.0
## - is_first_child:math_score 1 11.075 3768.9 1572.1
## - test_prep:is_first_child 1 11.352 3769.2 1572.2
## <none> 3757.9 1572.4
## - ethnic_group:math_score 4 51.893 3809.8 1572.5
## - wkly_study_hours:reading_score 2 26.204 3784.1 1572.5
## - gender:parent_marital_status 2 26.468 3784.3 1572.5
## - parent_educ:test_prep 5 65.923 3823.8 1572.6
## - parent_educ:lunch_type 5 69.778 3827.6 1573.2
## - practice_sport:is_first_child 2 31.312 3789.2 1573.3
## - ethnic_group:practice_sport 8 110.773 3868.6 1573.5
## - lunch_type:is_first_child 1 20.594 3778.5 1573.6
## - parent_educ:parent_marital_status 11 154.814 3912.7 1574.2
## - gender:reading_score 1 24.469 3782.3 1574.2
## - test_prep:practice_sport 2 47.385 3805.3 1575.8
## - ethnic_group:parent_marital_status 8 128.301 3886.2 1576.2
## - test_prep:transport_means 1 37.677 3795.5 1576.3
## - ethnic_group:parent_educ 20 295.100 4053.0 1577.0
## - math_score:reading_score 1 51.162 3809.0 1578.3
## - parent_marital_status:wkly_study_hours 4 106.504 3864.4 1580.9
## - ethnic_group:wkly_study_hours 8 162.721 3920.6 1581.4
## - parent_educ:practice_sport 10 189.415 3947.3 1581.4
## - test_prep:parent_marital_status 2 84.198 3842.1 1581.5
## + parent_educ:wkly_study_hours 10 62.949 3694.9 1582.4
## - ethnic_group:lunch_type 4 126.428 3884.3 1583.9
## - parent_educ:is_first_child 5 144.454 3902.3 1584.6
##
## Step: AIC=1566.69
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + ethnic_group:reading_score + parent_educ:lunch_type +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:reading_score 4 21.848 3807.3 1562.1
## - parent_educ:reading_score 5 35.036 3820.5 1562.1
## - parent_marital_status:practice_sport 4 22.902 3808.4 1562.2
## - practice_sport:wkly_study_hours 4 24.329 3809.8 1562.5
## - gender:practice_sport 2 0.752 3786.2 1562.8
## - parent_marital_status:is_first_child 2 1.148 3786.6 1562.9
## - test_prep:wkly_study_hours 2 2.059 3787.5 1563.0
## - ethnic_group:test_prep 4 27.986 3813.4 1563.0
## - parent_educ:math_score 5 42.626 3828.1 1563.3
## - practice_sport:transport_means 2 4.323 3789.8 1563.4
## - lunch_type:wkly_study_hours 2 7.364 3792.8 1563.8
## - practice_sport:reading_score 2 7.840 3793.3 1563.9
## - practice_sport:math_score 2 7.855 3793.3 1563.9
## - gender:wkly_study_hours 2 10.753 3796.2 1564.4
## - ethnic_group:transport_means 4 37.803 3823.3 1564.5
## - lunch_type:test_prep 1 0.035 3785.5 1564.7
## - lunch_type:transport_means 1 0.119 3785.6 1564.7
## - test_prep:math_score 1 0.127 3785.6 1564.7
## - lunch_type:reading_score 1 0.344 3785.8 1564.7
## - gender:test_prep 1 0.611 3786.1 1564.8
## - gender:lunch_type 1 0.838 3786.3 1564.8
## - test_prep:reading_score 1 0.959 3786.4 1564.8
## - transport_means:math_score 1 1.827 3787.3 1565.0
## - is_first_child:transport_means 1 2.402 3787.9 1565.1
## - transport_means:wkly_study_hours 2 15.509 3801.0 1565.1
## - parent_educ:transport_means 5 54.410 3839.9 1565.1
## - wkly_study_hours:math_score 2 15.608 3801.1 1565.1
## - parent_marital_status:transport_means 2 15.888 3801.3 1565.2
## - gender:transport_means 1 3.189 3788.6 1565.2
## - lunch_type:math_score 1 5.456 3790.9 1565.5
## - is_first_child:reading_score 1 6.047 3791.5 1565.6
## - lunch_type:practice_sport 2 19.737 3805.2 1565.8
## - is_first_child:wkly_study_hours 2 19.752 3805.2 1565.8
## - parent_educ:test_prep 5 58.890 3844.3 1565.8
## - gender:ethnic_group 4 46.932 3832.4 1566.0
## - lunch_type:parent_marital_status 2 21.839 3807.3 1566.1
## - gender:is_first_child 1 9.186 3794.6 1566.1
## - parent_marital_status:math_score 2 22.363 3807.8 1566.2
## - transport_means:reading_score 1 9.527 3795.0 1566.2
## - wkly_study_hours:reading_score 2 23.884 3809.3 1566.4
## - ethnic_group:is_first_child 4 50.203 3835.7 1566.5
## - ethnic_group:math_score 4 50.587 3836.0 1566.5
## - parent_marital_status:reading_score 2 24.912 3810.4 1566.6
## - gender:math_score 1 12.668 3798.1 1566.7
## - is_first_child:math_score 1 12.848 3798.3 1566.7
## <none> 3785.5 1566.7
## - test_prep:is_first_child 1 14.905 3800.4 1567.0
## - gender:parent_marital_status 2 30.128 3815.6 1567.4
## - practice_sport:is_first_child 2 31.109 3816.6 1567.5
## - parent_educ:lunch_type 5 70.249 3855.7 1567.5
## - lunch_type:is_first_child 1 20.847 3806.3 1567.9
## - parent_educ:parent_marital_status 11 153.429 3938.9 1568.1
## - ethnic_group:practice_sport 8 118.110 3903.6 1568.8
## - gender:reading_score 1 32.500 3818.0 1569.7
## - test_prep:practice_sport 2 45.736 3831.2 1569.8
## - test_prep:transport_means 1 41.797 3827.2 1571.2
## - ethnic_group:parent_educ 20 297.789 4083.2 1571.4
## - ethnic_group:parent_marital_status 8 137.109 3922.6 1571.7
## + gender:parent_educ 5 27.583 3757.9 1572.4
## - math_score:reading_score 1 60.046 3845.5 1574.0
## - parent_marital_status:wkly_study_hours 4 105.657 3891.1 1574.9
## - parent_educ:practice_sport 10 188.025 3973.5 1575.3
## + parent_educ:wkly_study_hours 10 67.747 3717.7 1576.0
## - test_prep:parent_marital_status 2 86.704 3872.2 1576.0
## - ethnic_group:wkly_study_hours 8 167.590 3953.0 1576.2
## - ethnic_group:lunch_type 4 126.481 3911.9 1578.1
## - parent_educ:is_first_child 5 161.474 3946.9 1581.3
##
## Step: AIC=1562.09
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 19.517 3826.8 1557.1
## - practice_sport:wkly_study_hours 4 22.287 3829.6 1557.5
## - gender:practice_sport 2 0.727 3808.0 1558.2
## - parent_marital_status:is_first_child 2 0.835 3808.1 1558.2
## - test_prep:wkly_study_hours 2 3.358 3810.7 1558.6
## - parent_educ:reading_score 5 42.868 3850.2 1558.7
## - lunch_type:wkly_study_hours 2 5.668 3813.0 1559.0
## - ethnic_group:test_prep 4 31.714 3839.0 1559.0
## - practice_sport:transport_means 2 5.795 3813.1 1559.0
## - parent_educ:math_score 5 46.199 3853.5 1559.2
## - gender:wkly_study_hours 2 7.331 3814.6 1559.2
## - practice_sport:math_score 2 7.774 3815.1 1559.3
## - practice_sport:reading_score 2 8.155 3815.5 1559.3
## - lunch_type:test_prep 1 0.000 3807.3 1560.1
## - test_prep:math_score 1 0.104 3807.4 1560.1
## - lunch_type:transport_means 1 0.201 3807.5 1560.1
## - lunch_type:reading_score 1 0.228 3807.5 1560.1
## - gender:test_prep 1 0.575 3807.9 1560.2
## - wkly_study_hours:math_score 2 13.544 3820.8 1560.2
## - gender:lunch_type 1 0.681 3808.0 1560.2
## - test_prep:reading_score 1 0.966 3808.3 1560.2
## - parent_marital_status:transport_means 2 14.336 3821.6 1560.3
## - transport_means:wkly_study_hours 2 14.614 3821.9 1560.3
## - is_first_child:transport_means 1 2.089 3809.4 1560.4
## - gender:transport_means 1 2.433 3809.7 1560.5
## - transport_means:math_score 1 2.986 3810.3 1560.5
## - lunch_type:practice_sport 2 16.302 3823.6 1560.6
## - is_first_child:reading_score 1 4.542 3811.8 1560.8
## - gender:ethnic_group 4 43.711 3851.0 1560.8
## - ethnic_group:transport_means 4 44.106 3851.4 1560.9
## - parent_educ:test_prep 5 57.889 3865.2 1561.0
## - parent_educ:transport_means 5 57.975 3865.3 1561.0
## - is_first_child:wkly_study_hours 2 19.406 3826.7 1561.1
## - transport_means:reading_score 1 6.499 3813.8 1561.1
## - lunch_type:math_score 1 6.660 3814.0 1561.1
## - lunch_type:parent_marital_status 2 20.900 3828.2 1561.3
## - wkly_study_hours:reading_score 2 21.824 3829.1 1561.5
## - gender:is_first_child 1 9.344 3816.6 1561.5
## - ethnic_group:is_first_child 4 48.365 3855.7 1561.5
## - parent_educ:parent_marital_status 11 142.875 3950.2 1561.8
## - parent_marital_status:math_score 2 25.313 3832.6 1562.0
## - is_first_child:math_score 1 12.668 3820.0 1562.0
## <none> 3807.3 1562.1
## - parent_marital_status:reading_score 2 27.775 3835.1 1562.4
## - test_prep:is_first_child 1 15.013 3822.3 1562.4
## - gender:math_score 1 15.416 3822.7 1562.5
## - parent_educ:lunch_type 5 69.639 3876.9 1562.8
## - lunch_type:is_first_child 1 18.473 3825.8 1562.9
## - gender:parent_marital_status 2 33.282 3840.6 1563.2
## - ethnic_group:practice_sport 8 114.716 3922.0 1563.6
## - practice_sport:is_first_child 2 36.899 3844.2 1563.8
## - ethnic_group:math_score 4 63.747 3871.0 1563.9
## - test_prep:practice_sport 2 41.275 3848.6 1564.5
## - ethnic_group:parent_marital_status 8 130.914 3938.2 1566.0
## - gender:reading_score 1 38.958 3846.3 1566.1
## + ethnic_group:reading_score 4 21.848 3785.5 1566.7
## - test_prep:transport_means 1 44.252 3851.6 1566.9
## + gender:parent_educ 5 26.709 3780.6 1567.9
## - ethnic_group:parent_educ 20 312.387 4119.7 1568.6
## - parent_educ:practice_sport 10 183.206 3990.5 1569.8
## - parent_marital_status:wkly_study_hours 4 107.527 3914.8 1570.5
## - test_prep:parent_marital_status 2 81.137 3888.4 1570.5
## - math_score:reading_score 1 69.969 3877.3 1570.8
## - ethnic_group:lunch_type 4 113.388 3920.7 1571.4
## + parent_educ:wkly_study_hours 10 63.592 3743.7 1572.2
## - ethnic_group:wkly_study_hours 8 178.272 3985.6 1573.1
## - parent_educ:is_first_child 5 156.726 3964.0 1575.9
##
## Step: AIC=1557.1
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:math_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 18.025 3844.8 1551.9
## - gender:practice_sport 2 1.095 3827.9 1553.3
## - parent_marital_status:is_first_child 2 1.795 3828.6 1553.4
## - ethnic_group:test_prep 4 30.097 3856.9 1553.7
## - lunch_type:wkly_study_hours 2 4.814 3831.6 1553.8
## - test_prep:wkly_study_hours 2 4.999 3831.8 1553.9
## - practice_sport:transport_means 2 5.016 3831.8 1553.9
## - parent_educ:math_score 5 46.122 3872.9 1554.2
## - parent_educ:reading_score 5 46.464 3873.3 1554.2
## - gender:wkly_study_hours 2 7.345 3834.2 1554.2
## - practice_sport:reading_score 2 8.089 3834.9 1554.3
## - practice_sport:math_score 2 8.347 3835.2 1554.4
## - wkly_study_hours:math_score 2 11.873 3838.7 1554.9
## - lunch_type:test_prep 1 0.018 3826.8 1555.1
## - test_prep:math_score 1 0.094 3826.9 1555.1
## - lunch_type:transport_means 1 0.172 3827.0 1555.1
## - lunch_type:reading_score 1 0.229 3827.0 1555.1
## - gender:lunch_type 1 0.259 3827.1 1555.1
## - parent_marital_status:transport_means 2 13.526 3840.3 1555.2
## - gender:test_prep 1 0.626 3827.4 1555.2
## - test_prep:reading_score 1 0.754 3827.6 1555.2
## - lunch_type:practice_sport 2 14.226 3841.0 1555.3
## - gender:transport_means 1 1.664 3828.5 1555.4
## - parent_educ:test_prep 5 54.465 3881.3 1555.4
## - is_first_child:transport_means 1 2.833 3829.7 1555.5
## - transport_means:wkly_study_hours 2 15.923 3842.7 1555.5
## - is_first_child:reading_score 1 3.373 3830.2 1555.6
## - transport_means:math_score 1 3.975 3830.8 1555.7
## - parent_educ:parent_marital_status 12 150.213 3977.0 1555.8
## - is_first_child:wkly_study_hours 2 17.974 3844.8 1555.9
## - parent_educ:transport_means 5 57.327 3884.1 1555.9
## - transport_means:reading_score 1 5.640 3832.5 1556.0
## - gender:ethnic_group 4 45.354 3872.2 1556.0
## - ethnic_group:is_first_child 4 45.507 3872.3 1556.1
## - lunch_type:math_score 1 6.782 3833.6 1556.2
## - wkly_study_hours:reading_score 2 19.985 3846.8 1556.2
## - gender:is_first_child 1 8.811 3835.6 1556.5
## - lunch_type:parent_marital_status 2 22.113 3848.9 1556.5
## - ethnic_group:transport_means 4 48.311 3875.1 1556.5
## - ethnic_group:practice_sport 8 103.054 3929.9 1556.8
## - is_first_child:math_score 1 12.164 3839.0 1557.0
## <none> 3826.8 1557.1
## - parent_marital_status:math_score 2 26.649 3853.5 1557.2
## - test_prep:is_first_child 1 15.821 3842.6 1557.5
## - gender:math_score 1 16.268 3843.1 1557.6
## - practice_sport:is_first_child 2 29.609 3856.4 1557.7
## - lunch_type:is_first_child 1 17.216 3844.0 1557.8
## - parent_marital_status:reading_score 2 30.657 3857.5 1557.8
## - parent_educ:lunch_type 5 73.755 3900.6 1558.4
## - gender:parent_marital_status 2 36.006 3862.8 1558.6
## - ethnic_group:math_score 4 62.740 3889.6 1558.7
## - test_prep:practice_sport 2 38.231 3865.0 1559.0
## - ethnic_group:parent_marital_status 8 131.658 3958.5 1561.1
## - gender:reading_score 1 39.188 3866.0 1561.1
## - test_prep:transport_means 1 42.256 3869.1 1561.6
## + parent_marital_status:practice_sport 4 19.517 3807.3 1562.1
## + ethnic_group:reading_score 4 18.462 3808.4 1562.2
## + gender:parent_educ 5 26.276 3800.5 1563.0
## - ethnic_group:parent_educ 20 311.069 4137.9 1563.2
## - test_prep:parent_marital_status 2 74.843 3901.7 1564.5
## - parent_educ:practice_sport 10 186.449 4013.3 1565.2
## - ethnic_group:lunch_type 4 112.206 3939.0 1566.2
## - parent_marital_status:wkly_study_hours 4 112.796 3939.6 1566.2
## - math_score:reading_score 1 73.484 3900.3 1566.3
## - ethnic_group:wkly_study_hours 8 172.145 3999.0 1567.1
## + parent_educ:wkly_study_hours 10 61.882 3764.9 1567.5
## - parent_educ:is_first_child 5 153.512 3980.3 1570.3
##
## Step: AIC=1551.88
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:math_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 1.082 3845.9 1548.0
## - parent_marital_status:is_first_child 2 1.118 3846.0 1548.0
## - ethnic_group:test_prep 4 30.233 3875.1 1548.5
## - practice_sport:transport_means 2 4.509 3849.4 1548.6
## - lunch_type:wkly_study_hours 2 4.510 3849.4 1548.6
## - test_prep:wkly_study_hours 2 5.395 3850.2 1548.7
## - gender:wkly_study_hours 2 9.380 3854.2 1549.3
## - practice_sport:reading_score 2 10.580 3855.4 1549.5
## - parent_educ:parent_marital_status 12 144.908 3989.7 1549.7
## - parent_marital_status:transport_means 2 12.048 3856.9 1549.7
## - practice_sport:math_score 2 12.381 3857.2 1549.8
## - test_prep:math_score 1 0.052 3844.9 1549.9
## - lunch_type:test_prep 1 0.069 3844.9 1549.9
## - parent_educ:math_score 5 52.567 3897.4 1549.9
## - lunch_type:transport_means 1 0.174 3845.0 1549.9
## - gender:test_prep 1 0.285 3845.1 1549.9
## - lunch_type:practice_sport 2 13.378 3858.2 1549.9
## - test_prep:reading_score 1 0.407 3845.2 1549.9
## - gender:lunch_type 1 0.441 3845.3 1549.9
## - lunch_type:reading_score 1 0.800 3845.6 1550.0
## - parent_educ:reading_score 5 53.793 3898.6 1550.1
## - gender:transport_means 1 1.347 3846.2 1550.1
## - wkly_study_hours:math_score 2 15.152 3860.0 1550.2
## - is_first_child:reading_score 1 2.575 3847.4 1550.3
## - is_first_child:transport_means 1 2.647 3847.5 1550.3
## - transport_means:wkly_study_hours 2 15.729 3860.6 1550.3
## - parent_educ:transport_means 5 55.877 3900.7 1550.4
## - parent_educ:test_prep 5 55.907 3900.7 1550.4
## - is_first_child:wkly_study_hours 2 16.988 3861.8 1550.5
## - gender:ethnic_group 4 43.367 3888.2 1550.5
## - transport_means:reading_score 1 4.536 3849.4 1550.6
## - transport_means:math_score 1 5.108 3850.0 1550.7
## - lunch_type:parent_marital_status 2 19.810 3864.7 1550.9
## - ethnic_group:transport_means 4 48.326 3893.2 1551.2
## - lunch_type:math_score 1 9.185 3854.0 1551.3
## - gender:is_first_child 1 9.191 3854.0 1551.3
## - ethnic_group:is_first_child 4 50.004 3894.8 1551.5
## - is_first_child:math_score 1 11.686 3856.5 1551.7
## - wkly_study_hours:reading_score 2 25.142 3870.0 1551.7
## - parent_marital_status:math_score 2 25.758 3870.6 1551.8
## - ethnic_group:practice_sport 8 105.352 3950.2 1551.8
## <none> 3844.8 1551.9
## - lunch_type:is_first_child 1 13.769 3858.6 1552.0
## - parent_marital_status:reading_score 2 28.803 3873.6 1552.3
## - practice_sport:is_first_child 2 29.437 3874.3 1552.4
## - test_prep:is_first_child 1 18.211 3863.1 1552.7
## - gender:math_score 1 18.609 3863.5 1552.7
## - parent_educ:lunch_type 5 73.363 3918.2 1553.0
## - gender:parent_marital_status 2 34.522 3879.4 1553.2
## - ethnic_group:math_score 4 64.766 3909.6 1553.7
## - test_prep:practice_sport 2 41.300 3886.1 1554.2
## - test_prep:transport_means 1 35.867 3880.7 1555.3
## - ethnic_group:parent_marital_status 8 134.014 3978.9 1556.1
## - gender:reading_score 1 40.787 3885.6 1556.1
## - ethnic_group:parent_educ 20 301.369 4146.2 1556.4
## + practice_sport:wkly_study_hours 4 18.025 3826.8 1557.1
## + ethnic_group:reading_score 4 16.858 3828.0 1557.3
## + parent_marital_status:practice_sport 4 15.254 3829.6 1557.5
## + gender:parent_educ 5 27.218 3817.6 1557.7
## - parent_educ:practice_sport 10 176.617 4021.5 1558.4
## - test_prep:parent_marital_status 2 76.631 3921.5 1559.5
## - parent_marital_status:wkly_study_hours 4 112.107 3956.9 1560.8
## - ethnic_group:lunch_type 4 113.404 3958.2 1561.0
## - math_score:reading_score 1 74.418 3919.3 1561.2
## - ethnic_group:wkly_study_hours 8 169.579 4014.4 1561.3
## + parent_educ:wkly_study_hours 10 61.641 3783.2 1562.3
## - parent_educ:is_first_child 5 158.255 4003.1 1565.7
##
## Step: AIC=1548.04
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:math_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:is_first_child 2 1.019 3846.9 1544.2
## - ethnic_group:test_prep 4 29.517 3875.4 1544.5
## - practice_sport:transport_means 2 4.532 3850.5 1544.7
## - lunch_type:wkly_study_hours 2 4.774 3850.7 1544.8
## - test_prep:wkly_study_hours 2 5.359 3851.3 1544.9
## - gender:wkly_study_hours 2 9.739 3855.7 1545.5
## - parent_marital_status:transport_means 2 11.254 3857.2 1545.8
## - parent_educ:parent_marital_status 12 144.358 3990.3 1545.8
## - parent_educ:math_score 5 52.097 3898.0 1546.0
## - lunch_type:test_prep 1 0.032 3846.0 1546.0
## - test_prep:math_score 1 0.060 3846.0 1546.0
## - lunch_type:transport_means 1 0.142 3846.1 1546.1
## - gender:test_prep 1 0.371 3846.3 1546.1
## - test_prep:reading_score 1 0.419 3846.3 1546.1
## - gender:lunch_type 1 0.563 3846.5 1546.1
## - parent_educ:reading_score 5 53.293 3899.2 1546.2
## - lunch_type:reading_score 1 0.836 3846.8 1546.2
## - gender:transport_means 1 1.264 3847.2 1546.2
## - lunch_type:practice_sport 2 15.034 3861.0 1546.3
## - wkly_study_hours:math_score 2 15.410 3861.3 1546.4
## - is_first_child:reading_score 1 2.619 3848.5 1546.4
## - parent_educ:test_prep 5 55.173 3901.1 1546.5
## - transport_means:wkly_study_hours 2 15.741 3861.7 1546.5
## - is_first_child:transport_means 1 2.749 3848.7 1546.5
## - is_first_child:wkly_study_hours 2 16.690 3862.6 1546.6
## - gender:ethnic_group 4 43.210 3889.1 1546.6
## - transport_means:reading_score 1 4.401 3850.3 1546.7
## - parent_educ:transport_means 5 57.717 3903.6 1546.8
## - transport_means:math_score 1 5.277 3851.2 1546.8
## - lunch_type:parent_marital_status 2 19.571 3865.5 1547.0
## - ethnic_group:transport_means 4 48.401 3894.3 1547.4
## - gender:is_first_child 1 9.365 3855.3 1547.5
## - lunch_type:math_score 1 9.667 3855.6 1547.5
## - ethnic_group:is_first_child 4 51.091 3897.0 1547.8
## - is_first_child:math_score 1 11.707 3857.6 1547.8
## - parent_marital_status:math_score 2 25.651 3871.6 1548.0
## - wkly_study_hours:reading_score 2 25.887 3871.8 1548.0
## <none> 3845.9 1548.0
## - lunch_type:is_first_child 1 13.737 3859.7 1548.2
## - ethnic_group:practice_sport 8 107.799 3953.7 1548.3
## - practice_sport:is_first_child 2 28.719 3874.6 1548.4
## - parent_marital_status:reading_score 2 28.944 3874.9 1548.5
## - practice_sport:reading_score 2 29.338 3875.3 1548.5
## - practice_sport:math_score 2 30.317 3876.2 1548.7
## - test_prep:is_first_child 1 17.830 3863.8 1548.8
## - gender:math_score 1 18.573 3864.5 1548.9
## - gender:parent_marital_status 2 35.200 3881.1 1549.4
## - parent_educ:lunch_type 5 74.905 3920.8 1549.4
## - ethnic_group:math_score 4 65.143 3911.1 1550.0
## - test_prep:practice_sport 2 42.773 3888.7 1550.6
## - test_prep:transport_means 1 35.208 3881.1 1551.4
## + gender:practice_sport 2 1.082 3844.8 1551.9
## - gender:reading_score 1 40.794 3886.7 1552.3
## - ethnic_group:parent_marital_status 8 134.792 3980.7 1552.4
## - ethnic_group:parent_educ 20 304.276 4150.2 1553.0
## + practice_sport:wkly_study_hours 4 18.013 3827.9 1553.3
## + ethnic_group:reading_score 4 17.130 3828.8 1553.4
## + parent_marital_status:practice_sport 4 15.684 3830.2 1553.6
## + gender:parent_educ 5 26.659 3819.3 1553.9
## - parent_educ:practice_sport 10 181.283 4027.2 1555.2
## - test_prep:parent_marital_status 2 76.039 3922.0 1555.6
## - parent_marital_status:wkly_study_hours 4 111.145 3957.1 1556.8
## - math_score:reading_score 1 75.125 3921.1 1557.5
## - ethnic_group:wkly_study_hours 8 169.288 4015.2 1557.5
## - ethnic_group:lunch_type 4 118.370 3964.3 1557.9
## + parent_educ:wkly_study_hours 10 62.312 3783.6 1558.4
## - parent_educ:is_first_child 5 158.649 4004.6 1561.9
##
## Step: AIC=1544.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 13 147.779 3994.7 1540.4
## - practice_sport:transport_means 2 4.396 3851.3 1540.9
## - ethnic_group:test_prep 4 30.876 3877.8 1540.9
## - lunch_type:wkly_study_hours 2 4.712 3851.7 1540.9
## - test_prep:wkly_study_hours 2 5.156 3852.1 1541.0
## - gender:wkly_study_hours 2 9.699 3856.6 1541.7
## - parent_marital_status:transport_means 2 10.858 3857.8 1541.9
## - parent_educ:math_score 5 52.088 3899.0 1542.1
## - lunch_type:test_prep 1 0.029 3847.0 1542.2
## - test_prep:math_score 1 0.060 3847.0 1542.2
## - lunch_type:transport_means 1 0.147 3847.1 1542.2
## - gender:test_prep 1 0.351 3847.3 1542.2
## - test_prep:reading_score 1 0.404 3847.3 1542.3
## - gender:lunch_type 1 0.632 3847.6 1542.3
## - lunch_type:reading_score 1 0.905 3847.8 1542.3
## - parent_educ:reading_score 5 53.702 3900.6 1542.4
## - gender:transport_means 1 1.240 3848.2 1542.4
## - lunch_type:practice_sport 2 14.629 3861.6 1542.4
## - transport_means:wkly_study_hours 2 15.129 3862.1 1542.5
## - parent_educ:test_prep 5 54.802 3901.7 1542.5
## - wkly_study_hours:math_score 2 15.346 3862.3 1542.5
## - is_first_child:reading_score 1 2.719 3849.7 1542.6
## - is_first_child:transport_means 1 2.791 3849.7 1542.6
## - is_first_child:wkly_study_hours 2 16.533 3863.5 1542.7
## - gender:ethnic_group 4 43.706 3890.6 1542.9
## - transport_means:reading_score 1 4.481 3851.4 1542.9
## - transport_means:math_score 1 5.187 3852.1 1543.0
## - parent_educ:transport_means 5 58.482 3905.4 1543.1
## - lunch_type:parent_marital_status 2 19.377 3866.3 1543.2
## - ethnic_group:transport_means 4 47.555 3894.5 1543.5
## - gender:is_first_child 1 9.746 3856.7 1543.7
## - lunch_type:math_score 1 10.005 3856.9 1543.7
## - is_first_child:math_score 1 11.394 3858.3 1543.9
## - wkly_study_hours:reading_score 2 25.453 3872.4 1544.1
## - parent_marital_status:math_score 2 25.778 3872.7 1544.1
## <none> 3846.9 1544.2
## - ethnic_group:is_first_child 4 52.718 3899.7 1544.2
## - lunch_type:is_first_child 1 13.501 3860.4 1544.3
## - ethnic_group:practice_sport 8 106.850 3953.8 1544.4
## - practice_sport:is_first_child 2 28.474 3875.4 1544.5
## - parent_marital_status:reading_score 2 28.823 3875.8 1544.6
## - practice_sport:reading_score 2 29.296 3876.2 1544.7
## - practice_sport:math_score 2 30.332 3877.3 1544.8
## - test_prep:is_first_child 1 17.346 3864.3 1544.8
## - gender:math_score 1 18.836 3865.8 1545.1
## - gender:parent_marital_status 2 34.722 3881.7 1545.5
## - parent_educ:lunch_type 5 75.245 3922.2 1545.6
## - ethnic_group:math_score 4 64.406 3911.3 1546.0
## - ethnic_group:parent_marital_status 9 135.974 3982.9 1546.7
## - test_prep:practice_sport 2 43.546 3890.5 1546.8
## - test_prep:transport_means 1 34.828 3881.8 1547.5
## + parent_marital_status:is_first_child 2 1.019 3845.9 1548.0
## + gender:practice_sport 2 0.983 3846.0 1548.0
## - gender:reading_score 1 40.892 3887.8 1548.4
## - ethnic_group:parent_educ 20 305.056 4152.0 1549.2
## + practice_sport:wkly_study_hours 4 17.389 3829.6 1549.5
## + ethnic_group:reading_score 4 16.843 3830.1 1549.6
## + parent_marital_status:practice_sport 4 16.397 3830.5 1549.7
## + gender:parent_educ 5 26.998 3819.9 1550.0
## - parent_educ:practice_sport 10 181.707 4028.7 1551.4
## - test_prep:parent_marital_status 2 76.167 3923.1 1551.8
## - parent_marital_status:wkly_study_hours 4 111.330 3958.3 1553.0
## - math_score:reading_score 1 75.584 3922.5 1553.7
## - ethnic_group:wkly_study_hours 8 170.355 4017.3 1553.8
## - ethnic_group:lunch_type 4 119.129 3966.1 1554.2
## + parent_educ:wkly_study_hours 10 62.794 3784.1 1554.5
## - parent_educ:is_first_child 5 161.530 4008.5 1558.5
##
## Step: AIC=1540.44
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 34.478 4029.2 1535.5
## - parent_marital_status:transport_means 3 12.388 4007.1 1536.3
## - gender:wkly_study_hours 2 6.072 4000.8 1537.3
## - lunch_type:wkly_study_hours 2 6.434 4001.2 1537.4
## - ethnic_group:test_prep 4 34.744 4029.5 1537.5
## - practice_sport:transport_means 2 8.185 4002.9 1537.7
## - parent_marital_status:math_score 3 22.557 4017.3 1537.8
## - test_prep:wkly_study_hours 2 9.134 4003.9 1537.8
## - wkly_study_hours:math_score 2 9.339 4004.1 1537.8
## - ethnic_group:parent_educ 20 261.812 4256.5 1537.9
## - is_first_child:wkly_study_hours 2 10.744 4005.5 1538.0
## - ethnic_group:practice_sport 8 93.525 4088.2 1538.1
## - parent_marital_status:reading_score 3 25.333 4020.1 1538.2
## - lunch_type:parent_marital_status 3 25.859 4020.6 1538.2
## - lunch_type:practice_sport 2 12.628 4007.3 1538.3
## - gender:test_prep 1 0.037 3994.8 1538.4
## - test_prep:reading_score 1 0.118 3994.8 1538.5
## - lunch_type:transport_means 1 0.173 3994.9 1538.5
## - test_prep:math_score 1 0.194 3994.9 1538.5
## - is_first_child:transport_means 1 0.311 3995.0 1538.5
## - is_first_child:reading_score 1 0.402 3995.1 1538.5
## - lunch_type:test_prep 1 0.439 3995.2 1538.5
## - gender:lunch_type 1 0.746 3995.5 1538.5
## - gender:transport_means 1 0.761 3995.5 1538.5
## - wkly_study_hours:reading_score 2 14.891 4009.6 1538.6
## - transport_means:reading_score 1 3.555 3998.3 1539.0
## - ethnic_group:parent_marital_status 11 141.689 4136.4 1539.0
## - gender:parent_marital_status 3 31.061 4025.8 1539.0
## - lunch_type:reading_score 1 4.323 3999.0 1539.1
## - is_first_child:math_score 1 4.379 3999.1 1539.1
## - gender:is_first_child 1 4.515 3999.2 1539.1
## - transport_means:math_score 1 5.313 4000.0 1539.2
## - ethnic_group:transport_means 4 47.799 4042.5 1539.5
## - parent_educ:reading_score 5 61.928 4056.7 1539.5
## - ethnic_group:is_first_child 4 52.682 4047.4 1540.2
## - parent_educ:transport_means 5 66.600 4061.3 1540.2
## - lunch_type:is_first_child 1 12.630 4007.4 1540.3
## - transport_means:wkly_study_hours 2 26.387 4021.1 1540.3
## <none> 3994.7 1540.4
## - lunch_type:math_score 1 15.303 4010.0 1540.7
## - gender:ethnic_group 4 58.078 4052.8 1541.0
## - parent_educ:math_score 5 71.907 4066.6 1541.0
## - test_prep:is_first_child 1 18.098 4012.8 1541.1
## - practice_sport:math_score 2 31.895 4026.6 1541.1
## - gender:math_score 1 19.962 4014.7 1541.4
## - parent_educ:lunch_type 5 75.243 4070.0 1541.5
## - practice_sport:reading_score 2 38.767 4033.5 1542.1
## - ethnic_group:math_score 4 69.183 4063.9 1542.6
## - practice_sport:is_first_child 2 41.813 4036.5 1542.6
## - test_prep:practice_sport 2 42.260 4037.0 1542.7
## - test_prep:transport_means 1 33.244 4028.0 1543.3
## + parent_educ:parent_marital_status 13 147.779 3846.9 1544.2
## + gender:practice_sport 2 0.663 3994.1 1544.3
## - test_prep:parent_marital_status 3 68.126 4062.8 1544.4
## - gender:reading_score 1 41.040 4035.8 1544.5
## - parent_marital_status:wkly_study_hours 6 111.050 4105.8 1544.6
## + parent_marital_status:is_first_child 3 4.440 3990.3 1545.8
## + gender:parent_educ 5 26.495 3968.2 1546.5
## + parent_marital_status:practice_sport 5 25.409 3969.3 1546.7
## + practice_sport:wkly_study_hours 4 11.502 3983.2 1546.7
## + ethnic_group:reading_score 4 7.731 3987.0 1547.3
## - ethnic_group:wkly_study_hours 8 161.021 4155.7 1547.8
## - ethnic_group:lunch_type 4 110.804 4105.5 1548.6
## - parent_educ:practice_sport 10 199.101 4193.8 1549.1
## - math_score:reading_score 1 76.170 4070.9 1549.6
## + parent_educ:wkly_study_hours 10 61.034 3933.7 1551.3
## - parent_educ:is_first_child 5 183.596 4178.3 1557.0
##
## Step: AIC=1535.51
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:math_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 13.099 4042.3 1531.4
## - ethnic_group:test_prep 4 29.957 4059.2 1531.9
## - practice_sport:transport_means 2 6.423 4035.6 1532.5
## - gender:wkly_study_hours 2 6.484 4035.7 1532.5
## - is_first_child:wkly_study_hours 2 6.642 4035.8 1532.5
## - test_prep:wkly_study_hours 2 6.717 4035.9 1532.5
## - lunch_type:wkly_study_hours 2 8.458 4037.7 1532.8
## - parent_marital_status:math_score 3 24.009 4053.2 1533.0
## - wkly_study_hours:math_score 2 11.932 4041.1 1533.2
## - ethnic_group:parent_educ 20 266.752 4296.0 1533.3
## - lunch_type:parent_marital_status 3 26.887 4056.1 1533.4
## - lunch_type:transport_means 1 0.037 4029.2 1533.5
## - is_first_child:transport_means 1 0.199 4029.4 1533.5
## - is_first_child:reading_score 1 0.303 4029.5 1533.5
## - gender:transport_means 1 0.411 4029.6 1533.6
## - test_prep:reading_score 1 0.412 4029.6 1533.6
## - gender:test_prep 1 0.429 4029.6 1533.6
## - lunch_type:test_prep 1 0.430 4029.6 1533.6
## - test_prep:math_score 1 0.551 4029.8 1533.6
## - parent_marital_status:reading_score 3 28.042 4057.2 1533.6
## - gender:lunch_type 1 0.738 4029.9 1533.6
## - lunch_type:practice_sport 2 15.473 4044.7 1533.8
## - gender:parent_marital_status 3 29.609 4058.8 1533.8
## - transport_means:reading_score 1 3.040 4032.2 1534.0
## - wkly_study_hours:reading_score 2 17.726 4046.9 1534.1
## - lunch_type:reading_score 1 4.090 4033.3 1534.1
## - is_first_child:math_score 1 4.182 4033.4 1534.1
## - gender:is_first_child 1 4.820 4034.0 1534.2
## - parent_educ:reading_score 5 60.012 4089.2 1534.2
## - ethnic_group:transport_means 4 47.080 4076.3 1534.4
## - transport_means:math_score 1 6.530 4035.7 1534.5
## - ethnic_group:practice_sport 8 104.117 4133.3 1534.6
## - ethnic_group:parent_marital_status 11 148.251 4177.5 1534.8
## - parent_educ:transport_means 5 67.389 4096.6 1535.3
## - lunch_type:is_first_child 1 12.329 4041.5 1535.3
## <none> 4029.2 1535.5
## - ethnic_group:is_first_child 4 55.136 4084.3 1535.5
## - transport_means:wkly_study_hours 2 28.271 4057.5 1535.6
## - lunch_type:math_score 1 14.553 4043.8 1535.6
## - gender:ethnic_group 4 56.172 4085.4 1535.7
## - test_prep:is_first_child 1 19.882 4049.1 1536.4
## - practice_sport:math_score 2 33.970 4063.2 1536.5
## - gender:math_score 1 20.739 4049.9 1536.5
## - ethnic_group:math_score 4 65.479 4094.7 1537.0
## - parent_educ:math_score 5 79.448 4108.6 1537.0
## - parent_educ:lunch_type 5 82.228 4111.4 1537.4
## - practice_sport:is_first_child 2 43.893 4073.1 1537.9
## - practice_sport:reading_score 2 44.302 4073.5 1538.0
## - test_prep:transport_means 1 31.485 4060.7 1538.1
## - test_prep:practice_sport 2 47.537 4076.7 1538.4
## - test_prep:parent_marital_status 3 63.701 4092.9 1538.8
## - gender:reading_score 1 39.019 4068.2 1539.2
## + gender:practice_sport 2 0.313 4028.9 1539.5
## - parent_marital_status:wkly_study_hours 6 110.748 4139.9 1539.5
## + parent_educ:test_prep 5 34.478 3994.7 1540.4
## + parent_marital_status:is_first_child 3 4.612 4024.6 1540.8
## + practice_sport:wkly_study_hours 4 12.948 4016.3 1541.6
## + parent_marital_status:practice_sport 5 21.986 4007.2 1542.3
## + ethnic_group:reading_score 4 7.461 4021.7 1542.4
## + parent_educ:parent_marital_status 13 127.454 3901.7 1542.5
## + gender:parent_educ 5 19.881 4009.3 1542.6
## - ethnic_group:wkly_study_hours 8 163.150 4192.3 1542.9
## - parent_educ:practice_sport 10 196.176 4225.4 1543.6
## - math_score:reading_score 1 75.442 4104.6 1544.5
## - ethnic_group:lunch_type 4 117.548 4146.7 1544.5
## + parent_educ:wkly_study_hours 10 61.686 3967.5 1546.4
## - parent_educ:is_first_child 5 179.211 4208.4 1551.2
##
## Step: AIC=1531.42
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## parent_marital_status:math_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 4.289 4046.6 1528.0
## - parent_marital_status:math_score 3 18.568 4060.9 1528.1
## - gender:wkly_study_hours 2 5.959 4048.3 1528.3
## - ethnic_group:test_prep 4 35.042 4077.3 1528.5
## - practice_sport:transport_means 2 7.582 4049.9 1528.5
## - test_prep:wkly_study_hours 2 8.091 4050.4 1528.6
## - lunch_type:wkly_study_hours 2 8.671 4051.0 1528.7
## - parent_marital_status:reading_score 3 22.745 4065.0 1528.7
## - lunch_type:parent_marital_status 3 22.856 4065.2 1528.8
## - wkly_study_hours:math_score 2 10.374 4052.7 1528.9
## - ethnic_group:parent_educ 20 266.664 4309.0 1529.1
## - lunch_type:transport_means 1 0.008 4042.3 1529.4
## - gender:transport_means 1 0.302 4042.6 1529.5
## - is_first_child:reading_score 1 0.336 4042.6 1529.5
## - is_first_child:transport_means 1 0.357 4042.7 1529.5
## - test_prep:reading_score 1 0.513 4042.8 1529.5
## - lunch_type:test_prep 1 0.589 4042.9 1529.5
## - gender:test_prep 1 0.696 4043.0 1529.5
## - gender:parent_marital_status 3 28.244 4070.5 1529.5
## - test_prep:math_score 1 0.818 4043.1 1529.5
## - gender:lunch_type 1 1.006 4043.3 1529.6
## - parent_educ:reading_score 5 57.074 4099.4 1529.7
## - lunch_type:practice_sport 2 15.986 4058.3 1529.8
## - wkly_study_hours:reading_score 2 16.460 4058.8 1529.8
## - transport_means:reading_score 1 2.838 4045.1 1529.8
## - lunch_type:reading_score 1 4.087 4046.4 1530.0
## - is_first_child:math_score 1 4.185 4046.5 1530.0
## - ethnic_group:practice_sport 8 101.856 4144.2 1530.1
## - gender:is_first_child 1 4.916 4047.2 1530.1
## - ethnic_group:transport_means 4 46.801 4089.1 1530.2
## - ethnic_group:parent_marital_status 11 145.809 4188.1 1530.3
## - transport_means:math_score 1 6.456 4048.8 1530.4
## - lunch_type:is_first_child 1 11.845 4054.1 1531.2
## - parent_educ:transport_means 5 67.513 4109.8 1531.2
## <none> 4042.3 1531.4
## - lunch_type:math_score 1 13.968 4056.3 1531.5
## - transport_means:wkly_study_hours 2 28.511 4070.8 1531.6
## - practice_sport:math_score 2 31.176 4073.5 1532.0
## - gender:math_score 1 17.692 4060.0 1532.0
## - gender:ethnic_group 4 60.187 4102.5 1532.1
## - ethnic_group:is_first_child 4 60.284 4102.6 1532.2
## - test_prep:is_first_child 1 20.279 4062.6 1532.4
## - parent_educ:math_score 5 77.463 4119.8 1532.6
## - parent_educ:lunch_type 5 79.757 4122.1 1533.0
## - test_prep:transport_means 1 26.682 4069.0 1533.3
## - ethnic_group:math_score 4 69.118 4111.4 1533.4
## - practice_sport:reading_score 2 42.942 4085.2 1533.7
## - practice_sport:is_first_child 2 43.391 4085.7 1533.7
## - test_prep:practice_sport 2 49.086 4091.4 1534.5
## - gender:reading_score 1 37.057 4079.4 1534.8
## - parent_marital_status:wkly_study_hours 6 108.596 4150.9 1535.1
## - test_prep:parent_marital_status 3 68.244 4110.5 1535.3
## + gender:practice_sport 2 0.218 4042.1 1535.4
## + parent_marital_status:transport_means 3 13.099 4029.2 1535.5
## + parent_educ:test_prep 5 35.189 4007.1 1536.3
## + parent_marital_status:is_first_child 3 7.416 4034.9 1536.3
## + practice_sport:wkly_study_hours 4 13.349 4029.0 1537.5
## + parent_marital_status:practice_sport 5 24.657 4017.6 1537.8
## + ethnic_group:reading_score 4 8.194 4034.1 1538.2
## + gender:parent_educ 5 18.451 4023.8 1538.7
## - parent_educ:practice_sport 10 192.112 4234.4 1538.8
## - ethnic_group:wkly_study_hours 8 165.310 4207.6 1539.1
## + parent_educ:parent_marital_status 14 131.161 3911.1 1540.0
## - ethnic_group:lunch_type 4 117.113 4159.4 1540.3
## - math_score:reading_score 1 76.701 4119.0 1540.5
## + parent_educ:wkly_study_hours 10 60.928 3981.4 1542.5
## - parent_educ:is_first_child 5 196.733 4239.0 1549.5
##
## Step: AIC=1528.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## parent_marital_status:math_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:math_score 3 16.905 4063.5 1524.5
## - gender:wkly_study_hours 2 5.613 4052.2 1524.9
## - test_prep:wkly_study_hours 2 7.030 4053.6 1525.1
## - parent_marital_status:reading_score 3 20.971 4067.6 1525.1
## - ethnic_group:test_prep 4 34.823 4081.4 1525.1
## - practice_sport:transport_means 2 7.866 4054.5 1525.2
## - lunch_type:wkly_study_hours 2 9.098 4055.7 1525.4
## - lunch_type:parent_marital_status 3 23.402 4070.0 1525.5
## - wkly_study_hours:math_score 2 10.191 4056.8 1525.5
## - ethnic_group:parent_educ 20 266.160 4312.7 1525.6
## - gender:parent_marital_status 3 26.455 4073.0 1525.9
## - lunch_type:transport_means 1 0.005 4046.6 1526.0
## - is_first_child:reading_score 1 0.149 4046.7 1526.1
## - gender:transport_means 1 0.300 4046.9 1526.1
## - is_first_child:transport_means 1 0.487 4047.1 1526.1
## - test_prep:reading_score 1 0.508 4047.1 1526.1
## - gender:test_prep 1 0.654 4047.2 1526.1
## - lunch_type:test_prep 1 0.709 4047.3 1526.2
## - test_prep:math_score 1 0.724 4047.3 1526.2
## - lunch_type:practice_sport 2 14.526 4061.1 1526.2
## - parent_educ:reading_score 5 56.397 4103.0 1526.2
## - gender:lunch_type 1 1.214 4047.8 1526.2
## - wkly_study_hours:reading_score 2 15.700 4062.3 1526.3
## - transport_means:reading_score 1 2.882 4049.5 1526.5
## - is_first_child:math_score 1 3.031 4049.6 1526.5
## - gender:is_first_child 1 3.819 4050.4 1526.6
## - lunch_type:reading_score 1 4.296 4050.9 1526.7
## - ethnic_group:practice_sport 8 101.764 4148.4 1526.7
## - ethnic_group:transport_means 4 47.072 4093.7 1526.9
## - transport_means:math_score 1 6.389 4053.0 1527.0
## - ethnic_group:parent_marital_status 11 150.842 4197.4 1527.6
## - lunch_type:is_first_child 1 11.722 4058.3 1527.8
## - parent_educ:transport_means 5 69.143 4115.7 1528.0
## <none> 4046.6 1528.0
## - lunch_type:math_score 1 14.188 4060.8 1528.1
## - transport_means:wkly_study_hours 2 29.647 4076.2 1528.4
## - gender:math_score 1 17.025 4063.6 1528.5
## - practice_sport:math_score 2 31.808 4078.4 1528.7
## - ethnic_group:is_first_child 4 59.782 4106.4 1528.7
## - parent_educ:math_score 5 75.889 4122.5 1529.0
## - gender:ethnic_group 4 62.431 4109.0 1529.1
## - test_prep:is_first_child 1 22.907 4069.5 1529.4
## - test_prep:transport_means 1 25.455 4072.0 1529.8
## - ethnic_group:math_score 4 69.141 4115.7 1530.0
## - parent_educ:lunch_type 5 83.150 4129.7 1530.0
## - practice_sport:is_first_child 2 43.979 4090.6 1530.4
## - practice_sport:reading_score 2 45.410 4092.0 1530.6
## - parent_marital_status:wkly_study_hours 6 105.886 4152.5 1531.3
## - test_prep:practice_sport 2 50.445 4097.0 1531.4
## - gender:reading_score 1 36.616 4083.2 1531.4
## + is_first_child:wkly_study_hours 2 4.289 4042.3 1531.4
## + gender:practice_sport 2 0.120 4046.5 1532.0
## - test_prep:parent_marital_status 3 69.789 4116.4 1532.1
## + parent_marital_status:transport_means 3 10.746 4035.8 1532.5
## + parent_marital_status:is_first_child 3 7.199 4039.4 1533.0
## + parent_educ:test_prep 5 31.560 4015.0 1533.4
## + practice_sport:wkly_study_hours 4 13.027 4033.6 1534.2
## + parent_marital_status:practice_sport 5 22.611 4024.0 1534.7
## + ethnic_group:reading_score 4 8.187 4038.4 1534.8
## - parent_educ:practice_sport 10 191.112 4237.7 1535.3
## + gender:parent_educ 5 17.816 4028.8 1535.5
## - ethnic_group:wkly_study_hours 8 164.190 4210.8 1535.5
## - ethnic_group:lunch_type 4 117.478 4164.1 1536.9
## - math_score:reading_score 1 75.541 4122.1 1537.0
## + parent_educ:parent_marital_status 14 127.310 3919.3 1537.2
## + parent_educ:wkly_study_hours 10 59.075 3987.5 1539.4
## - parent_educ:is_first_child 5 197.175 4243.8 1546.1
##
## Step: AIC=1524.51
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:reading_score 3 8.016 4071.5 1519.7
## - gender:parent_marital_status 3 15.793 4079.3 1520.8
## - gender:wkly_study_hours 2 6.548 4070.0 1521.5
## - ethnic_group:test_prep 4 34.618 4098.1 1521.5
## - lunch_type:wkly_study_hours 2 7.806 4071.3 1521.6
## - practice_sport:transport_means 2 7.846 4071.3 1521.7
## - test_prep:wkly_study_hours 2 8.694 4072.2 1521.8
## - wkly_study_hours:math_score 2 8.838 4072.3 1521.8
## - ethnic_group:practice_sport 8 96.102 4159.6 1522.3
## - lunch_type:practice_sport 2 13.480 4077.0 1522.5
## - lunch_type:transport_means 1 0.000 4063.5 1522.5
## - is_first_child:reading_score 1 0.002 4063.5 1522.5
## - gender:transport_means 1 0.026 4063.5 1522.5
## - gender:test_prep 1 0.356 4063.8 1522.6
## - test_prep:reading_score 1 0.357 4063.9 1522.6
## - test_prep:math_score 1 0.398 4063.9 1522.6
## - is_first_child:transport_means 1 0.659 4064.2 1522.6
## - wkly_study_hours:reading_score 2 14.737 4078.2 1522.6
## - lunch_type:test_prep 1 1.136 4064.6 1522.7
## - gender:lunch_type 1 1.802 4065.3 1522.8
## - is_first_child:math_score 1 1.883 4065.4 1522.8
## - transport_means:reading_score 1 2.159 4065.7 1522.8
## - gender:is_first_child 1 2.799 4066.3 1522.9
## - ethnic_group:parent_educ 20 273.729 4337.2 1523.0
## - parent_educ:reading_score 5 59.536 4123.0 1523.1
## - lunch_type:reading_score 1 4.466 4068.0 1523.2
## - ethnic_group:transport_means 4 47.199 4110.7 1523.3
## - transport_means:math_score 1 7.052 4070.5 1523.5
## - lunch_type:is_first_child 1 9.834 4073.3 1523.9
## - parent_educ:transport_means 5 67.293 4130.8 1524.2
## - gender:math_score 1 12.505 4076.0 1524.3
## <none> 4063.5 1524.5
## - lunch_type:math_score 1 14.283 4077.8 1524.6
## - ethnic_group:is_first_child 4 56.295 4119.8 1524.6
## - lunch_type:parent_marital_status 3 42.922 4106.4 1524.7
## - practice_sport:math_score 2 32.023 4095.5 1525.1
## - transport_means:wkly_study_hours 2 32.797 4096.3 1525.2
## - parent_educ:math_score 5 75.225 4138.7 1525.3
## - test_prep:is_first_child 1 23.691 4087.2 1525.9
## - test_prep:transport_means 1 24.426 4087.9 1526.0
## - gender:ethnic_group 4 66.343 4129.8 1526.1
## - ethnic_group:parent_marital_status 11 166.297 4229.8 1526.2
## - parent_educ:lunch_type 5 81.915 4145.4 1526.3
## - practice_sport:is_first_child 2 43.140 4106.6 1526.7
## - practice_sport:reading_score 2 44.198 4107.7 1526.9
## - parent_marital_status:wkly_study_hours 6 100.881 4164.4 1527.0
## - gender:reading_score 1 31.363 4094.9 1527.0
## - test_prep:practice_sport 2 49.638 4113.1 1527.7
## - ethnic_group:math_score 4 77.696 4141.2 1527.7
## + parent_marital_status:math_score 3 16.905 4046.6 1528.0
## + is_first_child:wkly_study_hours 2 2.626 4060.9 1528.1
## + gender:practice_sport 2 0.135 4063.4 1528.5
## - test_prep:parent_marital_status 3 69.990 4133.5 1528.6
## + parent_marital_status:is_first_child 3 6.727 4056.8 1529.5
## + parent_marital_status:transport_means 3 6.389 4057.1 1529.6
## + parent_educ:test_prep 5 33.306 4030.2 1529.7
## + practice_sport:wkly_study_hours 4 12.556 4050.9 1530.7
## + parent_marital_status:practice_sport 5 25.021 4038.5 1530.9
## + ethnic_group:reading_score 4 11.101 4052.4 1530.9
## + gender:parent_educ 5 18.043 4045.5 1531.9
## - parent_educ:practice_sport 10 194.319 4257.8 1532.1
## - ethnic_group:wkly_study_hours 8 165.976 4229.5 1532.1
## - math_score:reading_score 1 76.473 4140.0 1533.5
## - ethnic_group:lunch_type 4 121.687 4185.2 1533.9
## + parent_educ:wkly_study_hours 10 58.412 4005.1 1536.0
## + parent_educ:parent_marital_status 15 120.285 3943.2 1536.8
## - parent_educ:is_first_child 5 193.510 4257.0 1542.0
##
## Step: AIC=1519.67
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:is_first_child + gender:transport_means +
## gender:wkly_study_hours + gender:math_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 14.575 4086.1 1515.8
## - gender:wkly_study_hours 2 6.006 4077.5 1516.5
## - lunch_type:wkly_study_hours 2 7.571 4079.1 1516.8
## - practice_sport:transport_means 2 7.691 4079.2 1516.8
## - test_prep:wkly_study_hours 2 7.878 4079.4 1516.8
## - ethnic_group:test_prep 4 35.765 4107.3 1516.8
## - wkly_study_hours:math_score 2 8.990 4080.5 1517.0
## - ethnic_group:practice_sport 8 95.780 4167.3 1517.4
## - ethnic_group:parent_educ 20 270.182 4341.7 1517.6
## - lunch_type:practice_sport 2 13.520 4085.0 1517.6
## - gender:transport_means 1 0.000 4071.5 1517.7
## - lunch_type:transport_means 1 0.002 4071.5 1517.7
## - is_first_child:reading_score 1 0.036 4071.5 1517.7
## - gender:test_prep 1 0.463 4072.0 1517.7
## - test_prep:reading_score 1 0.624 4072.1 1517.8
## - test_prep:math_score 1 0.746 4072.3 1517.8
## - wkly_study_hours:reading_score 2 14.725 4086.2 1517.8
## - is_first_child:transport_means 1 0.931 4072.4 1517.8
## - lunch_type:test_prep 1 1.016 4072.5 1517.8
## - is_first_child:math_score 1 1.245 4072.8 1517.8
## - parent_educ:reading_score 5 57.213 4128.7 1517.9
## - gender:lunch_type 1 1.619 4073.1 1517.9
## - transport_means:reading_score 1 1.651 4073.2 1517.9
## - gender:is_first_child 1 2.094 4073.6 1518.0
## - lunch_type:reading_score 1 4.457 4076.0 1518.3
## - ethnic_group:transport_means 4 46.758 4118.3 1518.4
## - transport_means:math_score 1 7.658 4079.2 1518.8
## - lunch_type:is_first_child 1 10.204 4081.7 1519.2
## - parent_educ:transport_means 5 67.051 4138.6 1519.3
## - ethnic_group:is_first_child 4 54.591 4126.1 1519.5
## <none> 4071.5 1519.7
## - gender:math_score 1 14.695 4086.2 1519.8
## - lunch_type:math_score 1 14.958 4086.5 1519.8
## - lunch_type:parent_marital_status 3 43.116 4114.6 1519.9
## - transport_means:wkly_study_hours 2 32.982 4104.5 1520.4
## - parent_educ:math_score 5 75.385 4146.9 1520.5
## - ethnic_group:parent_marital_status 11 160.868 4232.4 1520.5
## - practice_sport:math_score 2 33.881 4105.4 1520.6
## - test_prep:transport_means 1 23.189 4094.7 1521.0
## - gender:ethnic_group 4 66.249 4137.8 1521.2
## - test_prep:is_first_child 1 26.218 4097.7 1521.5
## - parent_educ:lunch_type 5 83.672 4155.2 1521.7
## - ethnic_group:math_score 4 74.094 4145.6 1522.3
## - gender:reading_score 1 33.499 4105.0 1522.5
## - parent_marital_status:wkly_study_hours 6 103.837 4175.3 1522.5
## - practice_sport:reading_score 2 47.660 4119.2 1522.5
## - practice_sport:is_first_child 2 48.697 4120.2 1522.7
## - test_prep:practice_sport 2 51.071 4122.6 1523.0
## + is_first_child:wkly_study_hours 2 2.605 4068.9 1523.3
## + gender:practice_sport 2 0.129 4071.4 1523.7
## - test_prep:parent_marital_status 3 73.688 4145.2 1524.2
## + parent_marital_status:is_first_child 3 8.072 4063.4 1524.5
## + parent_educ:test_prep 5 35.478 4036.0 1524.5
## + parent_marital_status:reading_score 3 8.016 4063.5 1524.5
## + parent_marital_status:transport_means 3 7.020 4064.5 1524.7
## + parent_marital_status:math_score 3 3.950 4067.6 1525.1
## + parent_marital_status:practice_sport 5 27.303 4044.2 1525.7
## + ethnic_group:reading_score 4 11.931 4059.6 1525.9
## + practice_sport:wkly_study_hours 4 11.918 4059.6 1525.9
## - ethnic_group:wkly_study_hours 8 161.810 4233.3 1526.7
## + gender:parent_educ 5 18.003 4053.5 1527.1
## - parent_educ:practice_sport 10 196.144 4267.7 1527.4
## - ethnic_group:lunch_type 4 124.017 4195.5 1529.4
## - math_score:reading_score 1 87.496 4159.0 1530.2
## + parent_educ:wkly_study_hours 10 59.089 4012.4 1531.0
## + parent_educ:parent_marital_status 15 111.411 3960.1 1533.3
## - parent_educ:is_first_child 5 192.738 4264.2 1537.0
##
## Step: AIC=1515.78
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:math_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 5.512 4091.6 1512.6
## - lunch_type:wkly_study_hours 2 5.762 4091.8 1512.6
## - practice_sport:transport_means 2 7.031 4093.1 1512.8
## - test_prep:wkly_study_hours 2 7.301 4093.4 1512.8
## - wkly_study_hours:math_score 2 7.679 4093.8 1512.9
## - ethnic_group:parent_educ 20 268.754 4354.8 1513.4
## - lunch_type:practice_sport 2 13.035 4099.1 1513.7
## - wkly_study_hours:reading_score 2 13.656 4099.7 1513.8
## - gender:transport_means 1 0.046 4086.1 1513.8
## - is_first_child:reading_score 1 0.053 4086.1 1513.8
## - lunch_type:transport_means 1 0.091 4086.2 1513.8
## - ethnic_group:test_prep 4 41.971 4128.1 1513.8
## - gender:test_prep 1 0.696 4086.8 1513.9
## - test_prep:reading_score 1 0.722 4086.8 1513.9
## - lunch_type:test_prep 1 0.895 4087.0 1513.9
## - test_prep:math_score 1 0.903 4087.0 1513.9
## - is_first_child:math_score 1 1.026 4087.1 1513.9
## - is_first_child:transport_means 1 1.084 4087.2 1513.9
## - transport_means:reading_score 1 1.171 4087.3 1514.0
## - gender:lunch_type 1 1.502 4087.6 1514.0
## - gender:is_first_child 1 1.920 4088.0 1514.1
## - parent_educ:reading_score 5 58.777 4144.9 1514.2
## - ethnic_group:practice_sport 8 102.321 4188.4 1514.4
## - lunch_type:reading_score 1 4.119 4090.2 1514.4
## - ethnic_group:transport_means 4 50.821 4136.9 1515.1
## - transport_means:math_score 1 9.973 4096.1 1515.2
## - ethnic_group:parent_marital_status 11 152.415 4238.5 1515.4
## - lunch_type:is_first_child 1 11.454 4097.5 1515.4
## - parent_educ:transport_means 5 67.633 4153.7 1515.5
## - ethnic_group:is_first_child 4 54.067 4140.2 1515.5
## - gender:math_score 1 13.595 4099.7 1515.7
## <none> 4086.1 1515.8
## - lunch_type:parent_marital_status 3 42.590 4128.7 1515.9
## - lunch_type:math_score 1 15.038 4101.1 1516.0
## - parent_educ:math_score 5 73.970 4160.1 1516.4
## - transport_means:wkly_study_hours 2 32.491 4118.6 1516.5
## - practice_sport:math_score 2 36.233 4122.3 1517.0
## - test_prep:transport_means 1 22.978 4109.1 1517.1
## - gender:ethnic_group 4 67.060 4153.1 1517.4
## - test_prep:is_first_child 1 26.077 4112.2 1517.5
## - parent_educ:lunch_type 5 82.467 4168.6 1517.6
## - gender:reading_score 1 30.146 4116.2 1518.1
## - parent_marital_status:wkly_study_hours 6 101.482 4187.6 1518.2
## - practice_sport:reading_score 2 46.237 4132.3 1518.4
## - practice_sport:is_first_child 2 47.004 4133.1 1518.5
## - ethnic_group:math_score 4 77.107 4163.2 1518.8
## - test_prep:practice_sport 2 49.227 4135.3 1518.8
## + is_first_child:wkly_study_hours 2 2.178 4083.9 1519.5
## + gender:parent_marital_status 3 14.575 4071.5 1519.7
## + gender:practice_sport 2 0.236 4085.8 1519.8
## + parent_marital_status:is_first_child 3 7.843 4078.2 1520.7
## + parent_marital_status:transport_means 3 7.760 4078.3 1520.7
## + parent_marital_status:reading_score 3 6.798 4079.3 1520.8
## + parent_educ:test_prep 5 33.440 4052.6 1520.9
## - test_prep:parent_marital_status 3 80.664 4166.7 1521.3
## + parent_marital_status:math_score 3 2.616 4083.5 1521.4
## + parent_marital_status:practice_sport 5 26.833 4059.3 1521.9
## + ethnic_group:reading_score 4 12.980 4073.1 1521.9
## + practice_sport:wkly_study_hours 4 11.957 4074.1 1522.0
## + gender:parent_educ 5 18.543 4067.5 1523.1
## - ethnic_group:wkly_study_hours 8 166.181 4252.3 1523.3
## - parent_educ:practice_sport 10 197.482 4283.6 1523.6
## - ethnic_group:lunch_type 4 120.081 4206.2 1524.9
## + parent_educ:wkly_study_hours 10 61.936 4024.1 1526.8
## - math_score:reading_score 1 92.142 4178.2 1526.9
## + parent_educ:parent_marital_status 15 117.817 3968.3 1528.5
## - parent_educ:is_first_child 5 202.069 4288.2 1534.3
##
## Step: AIC=1512.58
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:wkly_study_hours 2 5.815 4097.4 1509.4
## - practice_sport:transport_means 2 6.684 4098.3 1509.5
## - test_prep:wkly_study_hours 2 8.558 4100.2 1509.8
## - wkly_study_hours:math_score 2 8.803 4100.4 1509.8
## - ethnic_group:parent_educ 20 268.329 4359.9 1510.0
## - lunch_type:practice_sport 2 12.525 4104.1 1510.4
## - gender:transport_means 1 0.130 4091.7 1510.6
## - lunch_type:transport_means 1 0.194 4091.8 1510.6
## - is_first_child:reading_score 1 0.197 4091.8 1510.6
## - gender:test_prep 1 0.616 4092.2 1510.7
## - lunch_type:test_prep 1 0.706 4092.3 1510.7
## - is_first_child:math_score 1 0.735 4092.3 1510.7
## - test_prep:reading_score 1 0.751 4092.3 1510.7
## - test_prep:math_score 1 0.881 4092.5 1510.7
## - transport_means:reading_score 1 0.975 4092.6 1510.7
## - is_first_child:transport_means 1 1.052 4092.6 1510.7
## - gender:lunch_type 1 1.248 4092.8 1510.8
## - gender:is_first_child 1 1.383 4093.0 1510.8
## - ethnic_group:test_prep 4 43.574 4135.2 1510.8
## - parent_educ:reading_score 5 59.416 4151.0 1511.1
## - wkly_study_hours:reading_score 2 18.133 4109.7 1511.2
## - lunch_type:reading_score 1 4.230 4095.8 1511.2
## - ethnic_group:practice_sport 8 103.982 4195.6 1511.4
## - ethnic_group:transport_means 4 51.106 4142.7 1511.9
## - lunch_type:is_first_child 1 10.887 4102.5 1512.1
## - transport_means:math_score 1 11.244 4102.8 1512.2
## - parent_educ:transport_means 5 67.329 4158.9 1512.2
## - lunch_type:parent_marital_status 3 41.514 4133.1 1512.5
## - ethnic_group:is_first_child 4 55.596 4147.2 1512.5
## - ethnic_group:parent_marital_status 11 155.240 4246.8 1512.5
## <none> 4091.6 1512.6
## - lunch_type:math_score 1 15.448 4107.0 1512.8
## - gender:math_score 1 16.544 4108.1 1513.0
## - transport_means:wkly_study_hours 2 34.330 4125.9 1513.5
## - parent_educ:math_score 5 77.091 4168.7 1513.6
## - practice_sport:math_score 2 35.312 4126.9 1513.7
## - gender:ethnic_group 4 64.232 4155.8 1513.8
## - test_prep:transport_means 1 22.453 4114.0 1513.8
## - parent_educ:lunch_type 5 79.920 4171.5 1514.0
## - test_prep:is_first_child 1 28.317 4119.9 1514.6
## - practice_sport:reading_score 2 44.650 4136.2 1515.0
## - ethnic_group:math_score 4 75.126 4166.7 1515.3
## - gender:reading_score 1 33.089 4124.7 1515.3
## - test_prep:practice_sport 2 47.506 4139.1 1515.4
## - parent_marital_status:wkly_study_hours 6 104.758 4196.4 1515.5
## - practice_sport:is_first_child 2 48.452 4140.0 1515.5
## + gender:wkly_study_hours 2 5.512 4086.1 1515.8
## + is_first_child:wkly_study_hours 2 1.855 4089.7 1516.3
## + gender:practice_sport 2 0.546 4091.1 1516.5
## + gender:parent_marital_status 3 14.081 4077.5 1516.5
## + parent_marital_status:is_first_child 3 7.848 4083.7 1517.4
## + parent_marital_status:transport_means 3 7.270 4084.3 1517.5
## + parent_marital_status:reading_score 3 6.400 4085.2 1517.7
## + parent_educ:test_prep 5 33.422 4058.2 1517.7
## + parent_marital_status:math_score 3 2.657 4088.9 1518.2
## - test_prep:parent_marital_status 3 81.548 4173.1 1518.2
## + parent_marital_status:practice_sport 5 27.453 4064.1 1518.6
## + practice_sport:wkly_study_hours 4 12.928 4078.7 1518.7
## + ethnic_group:reading_score 4 11.435 4080.2 1518.9
## + gender:parent_educ 5 19.118 4072.5 1519.8
## - ethnic_group:wkly_study_hours 8 164.492 4256.1 1519.8
## - parent_educ:practice_sport 10 198.898 4290.5 1520.6
## - ethnic_group:lunch_type 4 123.472 4215.1 1522.1
## - math_score:reading_score 1 91.900 4183.5 1523.7
## + parent_educ:wkly_study_hours 10 58.512 4033.1 1524.1
## + parent_educ:parent_marital_status 15 116.282 3975.3 1525.6
## - parent_educ:is_first_child 5 197.160 4288.8 1530.3
##
## Step: AIC=1509.41
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 263.576 4361.0 1506.2
## - wkly_study_hours:math_score 2 5.603 4103.0 1506.2
## - practice_sport:transport_means 2 7.004 4104.4 1506.4
## - test_prep:wkly_study_hours 2 9.331 4106.7 1506.8
## - lunch_type:practice_sport 2 13.567 4111.0 1507.4
## - gender:transport_means 1 0.139 4097.6 1507.4
## - is_first_child:reading_score 1 0.166 4097.6 1507.4
## - lunch_type:transport_means 1 0.310 4097.7 1507.5
## - lunch_type:test_prep 1 0.599 4098.0 1507.5
## - gender:test_prep 1 0.637 4098.0 1507.5
## - test_prep:reading_score 1 0.654 4098.1 1507.5
## - is_first_child:math_score 1 0.754 4098.2 1507.5
## - is_first_child:transport_means 1 0.796 4098.2 1507.5
## - test_prep:math_score 1 0.848 4098.3 1507.5
## - transport_means:reading_score 1 0.859 4098.3 1507.5
## - gender:lunch_type 1 0.903 4098.3 1507.5
## - gender:is_first_child 1 1.264 4098.7 1507.6
## - ethnic_group:test_prep 4 44.930 4142.3 1507.8
## - parent_educ:reading_score 5 59.115 4156.5 1507.9
## - lunch_type:reading_score 1 3.160 4100.6 1507.9
## - wkly_study_hours:reading_score 2 17.654 4115.1 1508.0
## - ethnic_group:practice_sport 8 103.007 4200.4 1508.1
## - parent_educ:transport_means 5 65.294 4162.7 1508.7
## - lunch_type:is_first_child 1 11.117 4108.5 1509.0
## - ethnic_group:transport_means 4 53.291 4150.7 1509.0
## - transport_means:math_score 1 11.931 4109.3 1509.1
## - ethnic_group:is_first_child 4 54.719 4152.1 1509.2
## - lunch_type:math_score 1 13.855 4111.3 1509.4
## <none> 4097.4 1509.4
## - lunch_type:parent_marital_status 3 43.170 4140.6 1509.6
## - ethnic_group:parent_marital_status 11 157.000 4254.4 1509.6
## - gender:math_score 1 17.375 4114.8 1509.9
## - parent_educ:math_score 5 75.257 4172.7 1510.2
## - transport_means:wkly_study_hours 2 34.080 4131.5 1510.3
## - practice_sport:math_score 2 34.227 4131.6 1510.3
## - gender:ethnic_group 4 65.052 4162.5 1510.7
## - parent_educ:lunch_type 5 79.850 4177.3 1510.8
## - test_prep:transport_means 1 25.068 4122.5 1511.0
## - practice_sport:reading_score 2 43.006 4140.4 1511.6
## - test_prep:is_first_child 1 29.814 4127.2 1511.7
## - parent_marital_status:wkly_study_hours 6 102.182 4199.6 1512.0
## - test_prep:practice_sport 2 46.263 4143.7 1512.0
## - gender:reading_score 1 35.094 4132.5 1512.4
## + lunch_type:wkly_study_hours 2 5.815 4091.6 1512.6
## + gender:wkly_study_hours 2 5.566 4091.8 1512.6
## - practice_sport:is_first_child 2 50.834 4148.2 1512.7
## - ethnic_group:math_score 4 79.418 4176.8 1512.7
## + is_first_child:wkly_study_hours 2 2.132 4095.3 1513.1
## + gender:practice_sport 2 0.708 4096.7 1513.3
## + gender:parent_marital_status 3 12.246 4085.2 1513.7
## + parent_marital_status:is_first_child 3 8.289 4089.1 1514.2
## + parent_educ:test_prep 5 35.209 4062.2 1514.3
## + parent_marital_status:transport_means 3 7.493 4089.9 1514.3
## + parent_marital_status:reading_score 3 6.629 4090.8 1514.5
## + parent_marital_status:math_score 3 2.609 4094.8 1515.0
## - test_prep:parent_marital_status 3 83.334 4180.7 1515.3
## + parent_marital_status:practice_sport 5 27.648 4069.8 1515.4
## + practice_sport:wkly_study_hours 4 12.169 4085.2 1515.7
## + ethnic_group:reading_score 4 10.902 4086.5 1515.8
## - ethnic_group:wkly_study_hours 8 160.497 4257.9 1516.1
## + gender:parent_educ 5 18.627 4078.8 1516.7
## - parent_educ:practice_sport 10 197.362 4294.8 1517.2
## - ethnic_group:lunch_type 4 126.663 4224.1 1519.4
## + parent_educ:wkly_study_hours 10 61.565 4035.8 1520.5
## - math_score:reading_score 1 96.451 4193.9 1521.1
## + parent_educ:parent_marital_status 15 115.485 3981.9 1522.5
## - parent_educ:is_first_child 5 200.148 4297.6 1527.5
##
## Step: AIC=1506.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 11 134.418 4495.4 1502.1
## - ethnic_group:transport_means 4 32.236 4393.2 1502.5
## - practice_sport:transport_means 2 5.631 4366.6 1503.0
## - wkly_study_hours:math_score 2 6.347 4367.3 1503.0
## - test_prep:wkly_study_hours 2 11.717 4372.7 1503.8
## - gender:transport_means 1 0.001 4361.0 1504.2
## - is_first_child:reading_score 1 0.511 4361.5 1504.3
## - is_first_child:transport_means 1 0.534 4361.5 1504.3
## - test_prep:reading_score 1 0.572 4361.6 1504.3
## - lunch_type:test_prep 1 0.970 4362.0 1504.3
## - gender:test_prep 1 0.988 4362.0 1504.3
## - gender:is_first_child 1 1.346 4362.3 1504.4
## - lunch_type:transport_means 1 1.360 4362.3 1504.4
## - transport_means:reading_score 1 1.361 4362.3 1504.4
## - gender:lunch_type 1 1.677 4362.7 1504.4
## - test_prep:math_score 1 1.705 4362.7 1504.4
## - lunch_type:practice_sport 2 17.004 4378.0 1504.5
## - lunch_type:is_first_child 1 2.606 4363.6 1504.5
## - ethnic_group:is_first_child 4 47.337 4408.3 1504.6
## - is_first_child:math_score 1 4.124 4365.1 1504.8
## - lunch_type:reading_score 1 5.589 4366.6 1505.0
## - wkly_study_hours:reading_score 2 21.181 4382.2 1505.0
## - transport_means:wkly_study_hours 2 22.891 4383.9 1505.3
## - lunch_type:parent_marital_status 3 38.402 4399.4 1505.4
## - ethnic_group:practice_sport 8 114.739 4475.7 1505.5
## - lunch_type:math_score 1 10.093 4371.1 1505.6
## - transport_means:math_score 1 10.722 4371.7 1505.6
## <none> 4361.0 1506.2
## - test_prep:transport_means 1 15.367 4376.4 1506.3
## - parent_educ:transport_means 5 76.924 4437.9 1506.5
## - ethnic_group:test_prep 4 62.614 4423.6 1506.6
## - gender:math_score 1 20.385 4381.4 1507.0
## - ethnic_group:wkly_study_hours 8 128.477 4489.5 1507.3
## - test_prep:is_first_child 1 25.974 4387.0 1507.7
## - test_prep:practice_sport 2 42.685 4403.7 1507.9
## - parent_educ:lunch_type 5 87.760 4448.7 1508.0
## - gender:reading_score 1 36.592 4397.6 1509.1
## - test_prep:parent_marital_status 3 68.234 4429.2 1509.4
## + ethnic_group:parent_educ 20 263.576 4097.4 1509.4
## + gender:wkly_study_hours 2 5.111 4355.9 1509.5
## + gender:practice_sport 2 2.941 4358.0 1509.8
## - practice_sport:reading_score 2 56.869 4417.9 1509.8
## + parent_educ:test_prep 5 45.848 4315.1 1510.0
## + is_first_child:wkly_study_hours 2 1.422 4359.6 1510.0
## + lunch_type:wkly_study_hours 2 1.063 4359.9 1510.0
## - practice_sport:math_score 2 61.393 4422.4 1510.4
## + gender:parent_marital_status 3 11.490 4349.5 1510.6
## + parent_marital_status:transport_means 3 10.758 4350.2 1510.7
## - gender:ethnic_group 4 96.203 4457.2 1511.1
## + ethnic_group:reading_score 4 21.138 4339.9 1511.3
## - practice_sport:is_first_child 2 68.564 4429.6 1511.4
## - parent_educ:practice_sport 10 190.937 4551.9 1511.5
## + parent_marital_status:reading_score 3 4.661 4356.3 1511.6
## + parent_marital_status:is_first_child 3 3.138 4357.9 1511.8
## - parent_educ:reading_score 5 117.945 4478.9 1511.9
## + parent_marital_status:math_score 3 1.533 4359.5 1512.0
## - ethnic_group:math_score 4 104.152 4465.1 1512.1
## - ethnic_group:lunch_type 4 108.376 4469.4 1512.7
## + parent_marital_status:practice_sport 5 24.797 4336.2 1512.8
## + practice_sport:wkly_study_hours 4 9.527 4351.5 1512.9
## - parent_marital_status:wkly_study_hours 6 144.757 4505.7 1513.5
## + gender:parent_educ 5 19.663 4341.3 1513.5
## - parent_educ:math_score 5 138.040 4499.0 1514.6
## - math_score:reading_score 1 81.843 4442.8 1515.2
## + parent_educ:wkly_study_hours 10 58.684 4302.3 1518.2
## + parent_educ:parent_marital_status 15 92.872 4268.1 1523.5
## - parent_educ:is_first_child 5 223.461 4584.4 1525.7
##
## Step: AIC=1502.11
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 6.574 4502.0 1499.0
## - ethnic_group:transport_means 4 38.691 4534.1 1499.2
## - wkly_study_hours:math_score 2 9.432 4504.8 1499.3
## - lunch_type:practice_sport 2 13.541 4508.9 1499.9
## - test_prep:wkly_study_hours 2 14.600 4510.0 1500.0
## - test_prep:reading_score 1 0.012 4495.4 1500.1
## - gender:transport_means 1 0.042 4495.4 1500.1
## - gender:test_prep 1 0.126 4495.5 1500.1
## - is_first_child:reading_score 1 0.144 4495.6 1500.1
## - gender:is_first_child 1 0.301 4495.7 1500.2
## - transport_means:reading_score 1 0.497 4495.9 1500.2
## - lunch_type:test_prep 1 0.545 4496.0 1500.2
## - test_prep:math_score 1 0.849 4496.3 1500.2
## - lunch_type:transport_means 1 1.070 4496.5 1500.2
## - is_first_child:transport_means 1 1.141 4496.5 1500.3
## - is_first_child:math_score 1 1.781 4497.2 1500.3
## - gender:lunch_type 1 2.369 4497.8 1500.4
## - ethnic_group:practice_sport 8 112.148 4607.6 1500.6
## - lunch_type:is_first_child 1 4.532 4499.9 1500.7
## - transport_means:wkly_study_hours 2 21.660 4517.1 1500.9
## - lunch_type:reading_score 1 8.568 4504.0 1501.2
## - ethnic_group:wkly_study_hours 8 119.694 4615.1 1501.6
## - wkly_study_hours:reading_score 2 26.990 4522.4 1501.6
## - lunch_type:math_score 1 12.057 4507.5 1501.7
## - transport_means:math_score 1 13.386 4508.8 1501.9
## <none> 4495.4 1502.1
## - gender:math_score 1 18.673 4514.1 1502.5
## - ethnic_group:test_prep 4 65.054 4560.5 1502.6
## - test_prep:transport_means 1 20.287 4515.7 1502.8
## - test_prep:practice_sport 2 36.294 4531.7 1502.8
## - test_prep:is_first_child 1 20.998 4516.4 1502.9
## - lunch_type:parent_marital_status 3 56.233 4551.6 1503.4
## - parent_educ:lunch_type 5 89.811 4585.2 1503.8
## - gender:reading_score 1 33.309 4528.7 1504.5
## - gender:ethnic_group 4 82.724 4578.1 1504.9
## + parent_educ:test_prep 5 54.502 4440.9 1504.9
## - practice_sport:reading_score 2 52.308 4547.7 1504.9
## - ethnic_group:lunch_type 4 83.783 4579.2 1505.0
## - ethnic_group:is_first_child 4 83.832 4579.2 1505.0
## + gender:wkly_study_hours 2 7.158 4488.2 1505.2
## - ethnic_group:math_score 4 87.135 4582.5 1505.4
## + lunch_type:wkly_study_hours 2 4.681 4490.7 1505.5
## - test_prep:parent_marital_status 3 72.321 4567.7 1505.5
## + gender:practice_sport 2 3.977 4491.4 1505.6
## + is_first_child:wkly_study_hours 2 3.785 4491.6 1505.6
## - practice_sport:math_score 2 58.279 4553.7 1505.7
## - parent_educ:reading_score 5 108.609 4604.0 1506.2
## + ethnic_group:parent_marital_status 11 134.418 4361.0 1506.2
## + parent_marital_status:math_score 3 12.758 4482.6 1506.4
## - parent_educ:transport_means 5 111.205 4606.6 1506.5
## + gender:parent_marital_status 3 9.390 4486.0 1506.9
## + parent_marital_status:is_first_child 3 8.174 4487.2 1507.0
## + parent_marital_status:transport_means 3 7.879 4487.5 1507.1
## + ethnic_group:reading_score 4 20.469 4474.9 1507.4
## + parent_marital_status:reading_score 3 4.279 4491.1 1507.5
## - practice_sport:is_first_child 2 74.367 4569.8 1507.8
## - parent_educ:practice_sport 10 201.040 4696.4 1507.9
## + gender:parent_educ 5 31.588 4463.8 1508.0
## + practice_sport:wkly_study_hours 4 10.191 4485.2 1508.8
## + ethnic_group:parent_educ 20 240.994 4254.4 1509.6
## + parent_marital_status:practice_sport 5 17.201 4478.2 1509.8
## - math_score:reading_score 1 75.306 4570.7 1509.9
## - parent_marital_status:wkly_study_hours 6 154.607 4650.0 1510.1
## - parent_educ:math_score 5 140.960 4636.4 1510.3
## + parent_educ:wkly_study_hours 10 55.302 4440.1 1514.8
## + parent_educ:parent_marital_status 15 96.005 4399.4 1519.4
## - parent_educ:is_first_child 5 232.016 4727.4 1521.8
##
## Step: AIC=1498.97
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:transport_means 4 39.294 4541.3 1496.1
## - wkly_study_hours:math_score 2 8.759 4510.7 1496.1
## - lunch_type:practice_sport 2 14.244 4516.2 1496.8
## - test_prep:wkly_study_hours 2 14.931 4516.9 1496.9
## - test_prep:reading_score 1 0.014 4502.0 1497.0
## - gender:transport_means 1 0.060 4502.0 1497.0
## - gender:test_prep 1 0.094 4502.1 1497.0
## - is_first_child:reading_score 1 0.164 4502.1 1497.0
## - lunch_type:test_prep 1 0.257 4502.2 1497.0
## - transport_means:reading_score 1 0.414 4502.4 1497.0
## - gender:is_first_child 1 0.417 4502.4 1497.0
## - test_prep:math_score 1 0.716 4502.7 1497.1
## - lunch_type:transport_means 1 1.196 4503.2 1497.1
## - is_first_child:transport_means 1 1.353 4503.3 1497.2
## - is_first_child:math_score 1 1.824 4503.8 1497.2
## - ethnic_group:practice_sport 8 110.626 4612.6 1497.3
## - gender:lunch_type 1 2.609 4504.6 1497.3
## - lunch_type:is_first_child 1 4.894 4506.9 1497.6
## - transport_means:wkly_study_hours 2 21.177 4523.2 1497.7
## - lunch_type:reading_score 1 9.135 4511.1 1498.2
## - wkly_study_hours:reading_score 2 25.732 4527.7 1498.3
## - ethnic_group:wkly_study_hours 8 119.308 4621.3 1498.4
## - lunch_type:math_score 1 13.188 4515.2 1498.7
## - transport_means:math_score 1 14.206 4516.2 1498.8
## <none> 4502.0 1499.0
## - ethnic_group:test_prep 4 64.842 4566.8 1499.4
## - gender:math_score 1 18.910 4520.9 1499.4
## - test_prep:transport_means 1 19.360 4521.3 1499.5
## - test_prep:practice_sport 2 36.247 4538.2 1499.7
## - test_prep:is_first_child 1 21.281 4523.3 1499.8
## - parent_educ:lunch_type 5 85.799 4587.8 1500.1
## - lunch_type:parent_marital_status 3 56.389 4558.4 1500.3
## - gender:reading_score 1 33.313 4535.3 1501.3
## - ethnic_group:lunch_type 4 81.670 4583.7 1501.6
## - ethnic_group:is_first_child 4 81.850 4583.8 1501.6
## - gender:ethnic_group 4 82.950 4584.9 1501.7
## - practice_sport:reading_score 2 52.533 4554.5 1501.8
## + gender:wkly_study_hours 2 7.571 4494.4 1502.0
## + practice_sport:transport_means 2 6.574 4495.4 1502.1
## + parent_educ:test_prep 5 51.220 4450.8 1502.2
## - ethnic_group:math_score 4 87.116 4589.1 1502.3
## + lunch_type:wkly_study_hours 2 5.277 4496.7 1502.3
## - test_prep:parent_marital_status 3 72.176 4574.2 1502.3
## + is_first_child:wkly_study_hours 2 4.127 4497.9 1502.4
## - parent_educ:reading_score 5 105.055 4607.0 1502.6
## - practice_sport:math_score 2 58.496 4560.5 1502.6
## + gender:practice_sport 2 1.476 4500.5 1502.8
## + ethnic_group:parent_marital_status 11 135.361 4366.6 1503.0
## + parent_marital_status:math_score 3 13.230 4488.7 1503.2
## - parent_educ:transport_means 5 110.982 4613.0 1503.3
## + gender:parent_marital_status 3 10.756 4491.2 1503.6
## + parent_marital_status:transport_means 3 8.613 4493.4 1503.8
## + parent_marital_status:is_first_child 3 8.082 4493.9 1503.9
## - practice_sport:is_first_child 2 68.870 4570.8 1503.9
## + ethnic_group:reading_score 4 20.497 4481.5 1504.3
## + parent_marital_status:reading_score 3 4.363 4497.6 1504.4
## + gender:parent_educ 5 30.245 4471.7 1505.0
## + practice_sport:wkly_study_hours 4 9.874 4492.1 1505.7
## + ethnic_group:parent_educ 20 239.979 4262.0 1506.7
## - parent_educ:practice_sport 10 216.463 4718.4 1506.7
## - parent_educ:math_score 5 137.228 4639.2 1506.7
## - parent_marital_status:wkly_study_hours 6 153.546 4655.5 1506.8
## - math_score:reading_score 1 77.678 4579.7 1507.1
## + parent_marital_status:practice_sport 5 14.426 4487.6 1507.1
## + parent_educ:wkly_study_hours 10 53.209 4448.8 1512.0
## + parent_educ:parent_marital_status 15 93.540 4408.4 1516.6
## - parent_educ:is_first_child 5 226.491 4728.5 1517.9
##
## Step: AIC=1496.1
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 96.429 4637.7 1492.5
## - wkly_study_hours:math_score 2 7.298 4548.6 1493.0
## - lunch_type:practice_sport 2 11.585 4552.9 1493.6
## - test_prep:reading_score 1 0.013 4541.3 1494.1
## - gender:transport_means 1 0.042 4541.3 1494.1
## - lunch_type:transport_means 1 0.102 4541.4 1494.1
## - test_prep:wkly_study_hours 2 15.638 4556.9 1494.1
## - is_first_child:transport_means 1 0.288 4541.6 1494.1
## - gender:test_prep 1 0.312 4541.6 1494.1
## - is_first_child:reading_score 1 0.396 4541.7 1494.2
## - lunch_type:test_prep 1 0.600 4541.9 1494.2
## - gender:is_first_child 1 0.755 4542.0 1494.2
## - test_prep:math_score 1 1.214 4542.5 1494.2
## - transport_means:reading_score 1 2.124 4543.4 1494.4
## - lunch_type:is_first_child 1 2.715 4544.0 1494.5
## - is_first_child:math_score 1 2.892 4544.2 1494.5
## - gender:lunch_type 1 3.521 4544.8 1494.5
## - wkly_study_hours:reading_score 2 20.590 4561.9 1494.8
## - transport_means:wkly_study_hours 2 20.818 4562.1 1494.8
## - transport_means:math_score 1 6.279 4547.6 1494.9
## - ethnic_group:wkly_study_hours 8 116.236 4657.5 1495.0
## - lunch_type:reading_score 1 9.568 4550.8 1495.3
## - lunch_type:math_score 1 14.031 4555.3 1495.9
## <none> 4541.3 1496.1
## - test_prep:transport_means 1 15.745 4557.0 1496.1
## - gender:math_score 1 17.894 4559.2 1496.4
## - test_prep:is_first_child 1 18.069 4559.3 1496.4
## - lunch_type:parent_marital_status 3 53.969 4595.2 1497.1
## - parent_educ:lunch_type 5 85.288 4626.6 1497.1
## - test_prep:practice_sport 2 38.672 4579.9 1497.1
## - ethnic_group:test_prep 4 72.370 4613.6 1497.4
## - ethnic_group:lunch_type 4 75.587 4616.9 1497.8
## - ethnic_group:math_score 4 78.862 4620.1 1498.2
## - gender:reading_score 1 33.037 4574.3 1498.4
## - gender:ethnic_group 4 81.290 4622.6 1498.6
## - ethnic_group:is_first_child 4 83.265 4624.5 1498.8
## + ethnic_group:transport_means 4 39.294 4502.0 1499.0
## - practice_sport:is_first_child 2 53.275 4594.5 1499.0
## - practice_sport:math_score 2 53.899 4595.2 1499.1
## + lunch_type:wkly_study_hours 2 7.667 4533.6 1499.1
## + practice_sport:transport_means 2 7.177 4534.1 1499.2
## + gender:wkly_study_hours 2 7.008 4534.3 1499.2
## - practice_sport:reading_score 2 55.144 4596.4 1499.2
## - parent_educ:reading_score 5 103.125 4644.4 1499.3
## + ethnic_group:parent_marital_status 11 141.691 4399.6 1499.4
## + is_first_child:wkly_study_hours 2 4.483 4536.8 1499.5
## - test_prep:parent_marital_status 3 73.182 4614.5 1499.5
## + gender:practice_sport 2 1.645 4539.6 1499.9
## + parent_educ:test_prep 5 47.414 4493.9 1499.9
## + parent_marital_status:math_score 3 13.231 4528.0 1500.4
## - parent_educ:transport_means 5 112.659 4653.9 1500.5
## + parent_marital_status:is_first_child 3 11.482 4529.8 1500.6
## + gender:parent_marital_status 3 11.307 4530.0 1500.6
## + ethnic_group:reading_score 4 25.545 4515.7 1500.8
## + parent_marital_status:transport_means 3 10.154 4531.1 1500.8
## + parent_marital_status:reading_score 3 4.706 4536.6 1501.5
## + gender:parent_educ 5 31.575 4509.7 1502.0
## + practice_sport:wkly_study_hours 4 13.182 4528.1 1502.4
## - parent_marital_status:wkly_study_hours 6 152.759 4694.0 1503.6
## + parent_marital_status:practice_sport 5 17.602 4523.7 1503.8
## - parent_educ:math_score 5 139.191 4680.5 1503.9
## - parent_educ:practice_sport 10 219.914 4761.2 1504.0
## - math_score:reading_score 1 81.156 4622.4 1504.5
## + ethnic_group:parent_educ 20 219.620 4321.7 1506.8
## + parent_educ:wkly_study_hours 10 50.863 4490.4 1509.5
## - parent_educ:is_first_child 5 212.675 4753.9 1513.1
## + parent_educ:parent_marital_status 15 94.199 4447.1 1513.7
##
## Step: AIC=1492.49
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:math_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:practice_sport 2 4.085 4641.8 1489.0
## - wkly_study_hours:math_score 2 6.449 4644.2 1489.3
## - lunch_type:transport_means 1 0.074 4637.8 1490.5
## - test_prep:reading_score 1 0.139 4637.8 1490.5
## - gender:test_prep 1 0.151 4637.9 1490.5
## - is_first_child:reading_score 1 0.249 4638.0 1490.5
## - gender:transport_means 1 0.278 4638.0 1490.5
## - is_first_child:transport_means 1 0.298 4638.0 1490.5
## - gender:is_first_child 1 0.505 4638.2 1490.6
## - test_prep:math_score 1 1.442 4639.1 1490.7
## - lunch_type:test_prep 1 1.951 4639.7 1490.7
## - is_first_child:math_score 1 2.153 4639.9 1490.8
## - transport_means:reading_score 1 2.187 4639.9 1490.8
## - lunch_type:is_first_child 1 2.476 4640.2 1490.8
## - wkly_study_hours:reading_score 2 19.258 4657.0 1490.9
## - gender:lunch_type 1 3.719 4641.4 1491.0
## - transport_means:math_score 1 4.069 4641.8 1491.0
## - ethnic_group:wkly_study_hours 8 115.791 4753.5 1491.0
## - lunch_type:reading_score 1 8.648 4646.4 1491.6
## - test_prep:wkly_study_hours 2 24.732 4662.4 1491.6
## - transport_means:wkly_study_hours 2 24.919 4662.6 1491.7
## - lunch_type:math_score 1 10.028 4647.7 1491.8
## - test_prep:transport_means 1 14.354 4652.1 1492.3
## - gender:math_score 1 15.348 4653.1 1492.4
## <none> 4637.7 1492.5
## - test_prep:is_first_child 1 16.028 4653.7 1492.5
## - practice_sport:math_score 2 36.073 4673.8 1493.1
## - ethnic_group:lunch_type 4 69.121 4706.8 1493.2
## - test_prep:practice_sport 2 38.874 4676.6 1493.4
## - practice_sport:is_first_child 2 39.068 4676.8 1493.4
## - ethnic_group:test_prep 4 72.397 4710.1 1493.6
## - lunch_type:parent_marital_status 3 59.365 4697.1 1494.0
## - test_prep:parent_marital_status 3 61.317 4699.0 1494.2
## - practice_sport:reading_score 2 46.317 4684.0 1494.4
## - parent_educ:reading_score 5 95.049 4732.8 1494.5
## + parent_educ:test_prep 5 62.211 4575.5 1494.5
## - parent_educ:lunch_type 5 95.606 4733.3 1494.5
## - ethnic_group:is_first_child 4 80.750 4718.5 1494.7
## - ethnic_group:math_score 4 81.516 4719.2 1494.8
## - gender:reading_score 1 35.259 4673.0 1495.0
## - parent_educ:transport_means 5 99.690 4737.4 1495.0
## + lunch_type:wkly_study_hours 2 10.433 4627.3 1495.2
## - gender:ethnic_group 4 86.497 4724.2 1495.4
## + gender:wkly_study_hours 2 6.782 4630.9 1495.6
## + practice_sport:transport_means 2 4.487 4633.2 1495.9
## + is_first_child:wkly_study_hours 2 4.122 4633.6 1496.0
## + ethnic_group:practice_sport 8 96.429 4541.3 1496.1
## + gender:practice_sport 2 0.947 4636.8 1496.4
## + parent_marital_status:is_first_child 3 15.429 4622.3 1496.5
## + gender:parent_marital_status 3 14.004 4623.7 1496.7
## + ethnic_group:parent_marital_status 11 137.275 4500.4 1496.8
## + parent_marital_status:math_score 3 9.548 4628.2 1497.3
## + ethnic_group:transport_means 4 25.098 4612.6 1497.3
## + gender:parent_educ 5 39.651 4598.1 1497.4
## + parent_marital_status:reading_score 3 4.793 4632.9 1497.9
## + parent_marital_status:transport_means 3 4.767 4632.9 1497.9
## + ethnic_group:reading_score 4 19.236 4618.5 1498.0
## + practice_sport:wkly_study_hours 4 16.993 4620.7 1498.3
## - parent_educ:math_score 5 126.716 4764.4 1498.4
## - math_score:reading_score 1 72.425 4710.1 1499.6
## - parent_marital_status:wkly_study_hours 6 155.932 4793.6 1500.0
## + parent_marital_status:practice_sport 5 9.052 4628.7 1501.3
## + ethnic_group:parent_educ 20 230.479 4407.2 1502.4
## - parent_educ:practice_sport 10 241.622 4879.3 1502.5
## + parent_educ:wkly_study_hours 10 50.368 4587.3 1506.0
## - parent_educ:is_first_child 5 204.434 4842.1 1507.9
## + parent_educ:parent_marital_status 15 86.973 4550.7 1511.3
##
## Step: AIC=1489.01
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:math_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - wkly_study_hours:math_score 2 6.427 4648.2 1485.8
## - gender:test_prep 1 0.123 4641.9 1487.0
## - test_prep:reading_score 1 0.140 4641.9 1487.0
## - lunch_type:transport_means 1 0.149 4641.9 1487.0
## - is_first_child:reading_score 1 0.231 4642.0 1487.0
## - gender:transport_means 1 0.288 4642.1 1487.0
## - is_first_child:transport_means 1 0.312 4642.1 1487.0
## - gender:is_first_child 1 0.860 4642.6 1487.1
## - test_prep:math_score 1 1.461 4643.2 1487.2
## - is_first_child:math_score 1 2.168 4644.0 1487.3
## - transport_means:reading_score 1 2.209 4644.0 1487.3
## - lunch_type:test_prep 1 2.407 4644.2 1487.3
## - lunch_type:is_first_child 1 2.689 4644.5 1487.3
## - wkly_study_hours:reading_score 2 19.621 4661.4 1487.5
## - gender:lunch_type 1 4.059 4645.8 1487.5
## - transport_means:math_score 1 4.252 4646.0 1487.5
## - ethnic_group:wkly_study_hours 8 119.442 4761.2 1488.0
## - transport_means:wkly_study_hours 2 24.620 4666.4 1488.1
## - lunch_type:reading_score 1 8.850 4650.6 1488.1
## - test_prep:wkly_study_hours 2 24.865 4666.7 1488.2
## - lunch_type:math_score 1 10.454 4652.2 1488.3
## - test_prep:transport_means 1 14.600 4656.4 1488.9
## - gender:math_score 1 15.269 4657.1 1489.0
## <none> 4641.8 1489.0
## - test_prep:is_first_child 1 16.166 4658.0 1489.1
## - practice_sport:math_score 2 36.464 4678.3 1489.6
## - ethnic_group:lunch_type 4 68.330 4710.1 1489.6
## - practice_sport:is_first_child 2 38.300 4680.1 1489.9
## - test_prep:practice_sport 2 40.658 4682.4 1490.2
## - lunch_type:parent_marital_status 3 57.927 4699.7 1490.3
## - ethnic_group:test_prep 4 75.611 4717.4 1490.5
## - test_prep:parent_marital_status 3 61.908 4703.7 1490.8
## - practice_sport:reading_score 2 46.395 4688.2 1490.9
## + parent_educ:test_prep 5 61.804 4580.0 1491.1
## - parent_educ:lunch_type 5 97.292 4739.1 1491.2
## - ethnic_group:math_score 4 81.582 4723.4 1491.3
## - ethnic_group:is_first_child 4 82.123 4723.9 1491.4
## - gender:reading_score 1 34.973 4676.8 1491.4
## - parent_educ:reading_score 5 98.886 4740.7 1491.5
## - parent_educ:transport_means 5 99.299 4741.1 1491.5
## + lunch_type:wkly_study_hours 2 11.648 4630.1 1491.5
## - gender:ethnic_group 4 85.470 4727.3 1491.8
## + gender:wkly_study_hours 2 6.493 4635.3 1492.2
## + practice_sport:transport_means 2 4.564 4637.2 1492.4
## + lunch_type:practice_sport 2 4.085 4637.7 1492.5
## + is_first_child:wkly_study_hours 2 3.504 4638.3 1492.6
## + gender:practice_sport 2 0.821 4641.0 1492.9
## + parent_marital_status:is_first_child 3 15.435 4626.4 1493.0
## + gender:parent_marital_status 3 11.727 4630.1 1493.5
## + ethnic_group:practice_sport 8 88.930 4552.9 1493.6
## + parent_marital_status:math_score 3 9.220 4632.6 1493.8
## + ethnic_group:transport_means 4 24.602 4617.2 1493.9
## + ethnic_group:parent_marital_status 11 132.686 4509.1 1493.9
## + gender:parent_educ 5 40.019 4601.8 1493.9
## + parent_marital_status:transport_means 3 5.189 4636.6 1494.3
## + parent_marital_status:reading_score 3 4.223 4637.6 1494.5
## + practice_sport:wkly_study_hours 4 18.074 4623.7 1494.7
## + ethnic_group:reading_score 4 17.890 4623.9 1494.7
## - parent_educ:math_score 5 132.009 4773.8 1495.6
## - math_score:reading_score 1 74.022 4715.8 1496.3
## - parent_marital_status:wkly_study_hours 6 156.704 4798.5 1496.6
## + parent_marital_status:practice_sport 5 8.623 4633.2 1497.9
## - parent_educ:practice_sport 10 240.847 4882.6 1498.9
## + ethnic_group:parent_educ 20 230.953 4410.8 1498.9
## + parent_educ:wkly_study_hours 10 50.143 4591.6 1502.6
## - parent_educ:is_first_child 5 204.050 4845.8 1504.4
## + parent_educ:parent_marital_status 15 86.947 4554.8 1507.9
##
## Step: AIC=1485.83
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 0.026 4648.2 1483.8
## - gender:test_prep 1 0.071 4648.3 1483.8
## - is_first_child:transport_means 1 0.110 4648.3 1483.8
## - test_prep:reading_score 1 0.220 4648.4 1483.9
## - is_first_child:reading_score 1 0.227 4648.4 1483.9
## - gender:transport_means 1 0.389 4648.6 1483.9
## - gender:is_first_child 1 0.786 4649.0 1483.9
## - test_prep:math_score 1 1.079 4649.3 1484.0
## - lunch_type:test_prep 1 2.009 4650.2 1484.1
## - is_first_child:math_score 1 2.350 4650.6 1484.1
## - lunch_type:is_first_child 1 2.799 4651.0 1484.2
## - transport_means:reading_score 1 2.907 4651.1 1484.2
## - wkly_study_hours:reading_score 2 19.694 4667.9 1484.3
## - transport_means:math_score 1 3.933 4652.1 1484.3
## - gender:lunch_type 1 4.189 4652.4 1484.4
## - ethnic_group:wkly_study_hours 8 119.047 4767.3 1484.8
## - lunch_type:reading_score 1 8.695 4656.9 1484.9
## - test_prep:wkly_study_hours 2 25.007 4673.2 1485.0
## - transport_means:wkly_study_hours 2 25.270 4673.5 1485.0
## - lunch_type:math_score 1 10.472 4658.7 1485.2
## - test_prep:is_first_child 1 14.916 4663.1 1485.7
## - test_prep:transport_means 1 14.951 4663.2 1485.7
## <none> 4648.2 1485.8
## - gender:math_score 1 15.820 4664.0 1485.8
## - ethnic_group:lunch_type 4 67.085 4715.3 1486.3
## - practice_sport:is_first_child 2 37.888 4686.1 1486.6
## - practice_sport:math_score 2 37.997 4686.2 1486.6
## - test_prep:practice_sport 2 40.293 4688.5 1486.9
## - lunch_type:parent_marital_status 3 56.961 4705.2 1487.0
## - ethnic_group:test_prep 4 77.070 4725.3 1487.5
## - ethnic_group:is_first_child 4 78.587 4726.8 1487.7
## - test_prep:parent_marital_status 3 62.700 4710.9 1487.7
## - practice_sport:reading_score 2 47.095 4695.3 1487.8
## - parent_educ:reading_score 5 95.264 4743.5 1487.8
## + parent_educ:test_prep 5 62.680 4585.5 1487.8
## - ethnic_group:math_score 4 80.544 4728.8 1488.0
## - parent_educ:lunch_type 5 97.718 4745.9 1488.1
## - gender:reading_score 1 35.271 4683.5 1488.3
## - gender:ethnic_group 4 83.861 4732.1 1488.4
## - parent_educ:transport_means 5 101.826 4750.0 1488.6
## + lunch_type:wkly_study_hours 2 7.442 4640.8 1488.9
## + gender:wkly_study_hours 2 6.525 4641.7 1489.0
## + wkly_study_hours:math_score 2 6.427 4641.8 1489.0
## + lunch_type:practice_sport 2 4.062 4644.2 1489.3
## + practice_sport:transport_means 2 4.015 4644.2 1489.3
## + is_first_child:wkly_study_hours 2 3.694 4644.5 1489.4
## + parent_marital_status:is_first_child 3 16.635 4631.6 1489.7
## + gender:practice_sport 2 0.686 4647.5 1489.7
## + gender:parent_marital_status 3 10.989 4637.2 1490.4
## + ethnic_group:parent_marital_status 11 134.787 4513.4 1490.5
## + ethnic_group:practice_sport 8 88.305 4559.9 1490.5
## + parent_marital_status:math_score 3 9.142 4639.1 1490.7
## + gender:parent_educ 5 39.318 4608.9 1490.8
## + ethnic_group:transport_means 4 23.168 4625.0 1490.9
## + parent_marital_status:transport_means 3 4.747 4643.5 1491.2
## + parent_marital_status:reading_score 3 3.854 4644.4 1491.3
## + practice_sport:wkly_study_hours 4 18.055 4630.2 1491.5
## + ethnic_group:reading_score 4 16.389 4631.8 1491.7
## - parent_educ:math_score 5 127.156 4775.4 1491.8
## - parent_marital_status:wkly_study_hours 6 155.995 4804.2 1493.3
## - math_score:reading_score 1 79.762 4728.0 1493.9
## + parent_marital_status:practice_sport 5 7.945 4640.3 1494.8
## - parent_educ:practice_sport 10 238.468 4886.7 1495.3
## + ethnic_group:parent_educ 20 230.919 4417.3 1495.8
## + parent_educ:wkly_study_hours 10 50.066 4598.1 1499.4
## - parent_educ:is_first_child 5 206.513 4854.7 1501.5
## + parent_educ:parent_marital_status 15 86.486 4561.7 1504.8
##
## Step: AIC=1483.83
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:is_first_child + gender:transport_means + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 0.074 4648.3 1481.8
## - is_first_child:transport_means 1 0.107 4648.3 1481.8
## - test_prep:reading_score 1 0.213 4648.5 1481.9
## - is_first_child:reading_score 1 0.221 4648.5 1481.9
## - gender:transport_means 1 0.371 4648.6 1481.9
## - gender:is_first_child 1 0.770 4649.0 1481.9
## - test_prep:math_score 1 1.087 4649.3 1482.0
## - lunch_type:test_prep 1 1.983 4650.2 1482.1
## - is_first_child:math_score 1 2.331 4650.6 1482.1
## - lunch_type:is_first_child 1 2.822 4651.1 1482.2
## - transport_means:reading_score 1 2.894 4651.1 1482.2
## - wkly_study_hours:reading_score 2 19.712 4668.0 1482.3
## - gender:lunch_type 1 4.164 4652.4 1482.4
## - transport_means:math_score 1 4.562 4652.8 1482.4
## - ethnic_group:wkly_study_hours 8 119.025 4767.3 1482.8
## - lunch_type:reading_score 1 8.684 4656.9 1482.9
## - test_prep:wkly_study_hours 2 25.028 4673.3 1483.0
## - transport_means:wkly_study_hours 2 25.263 4673.5 1483.0
## - lunch_type:math_score 1 10.448 4658.7 1483.2
## - test_prep:is_first_child 1 14.891 4663.1 1483.7
## - test_prep:transport_means 1 15.219 4663.5 1483.8
## <none> 4648.2 1483.8
## - gender:math_score 1 15.824 4664.1 1483.8
## - ethnic_group:lunch_type 4 67.082 4715.3 1484.3
## - practice_sport:math_score 2 37.978 4686.2 1484.6
## - practice_sport:is_first_child 2 38.149 4686.4 1484.7
## - test_prep:practice_sport 2 40.583 4688.8 1485.0
## - lunch_type:parent_marital_status 3 57.060 4705.3 1485.0
## - ethnic_group:test_prep 4 77.046 4725.3 1485.5
## - ethnic_group:is_first_child 4 78.561 4726.8 1485.7
## - test_prep:parent_marital_status 3 62.818 4711.1 1485.8
## - practice_sport:reading_score 2 47.096 4695.3 1485.8
## - parent_educ:reading_score 5 95.258 4743.5 1485.8
## + lunch_type:transport_means 1 0.026 4648.2 1485.8
## + parent_educ:test_prep 5 62.521 4585.7 1485.8
## - ethnic_group:math_score 4 81.338 4729.6 1486.1
## - parent_educ:lunch_type 5 98.765 4747.0 1486.2
## - gender:reading_score 1 35.292 4683.5 1486.3
## - gender:ethnic_group 4 83.902 4732.1 1486.4
## - parent_educ:transport_means 5 102.584 4750.8 1486.7
## + lunch_type:wkly_study_hours 2 7.468 4640.8 1486.9
## + gender:wkly_study_hours 2 6.486 4641.8 1487.0
## + wkly_study_hours:math_score 2 6.304 4641.9 1487.0
## + lunch_type:practice_sport 2 4.085 4644.2 1487.3
## + practice_sport:transport_means 2 4.015 4644.2 1487.3
## + is_first_child:wkly_study_hours 2 3.683 4644.6 1487.4
## + parent_marital_status:is_first_child 3 16.654 4631.6 1487.7
## + gender:practice_sport 2 0.680 4647.6 1487.8
## + gender:parent_marital_status 3 11.007 4637.2 1488.4
## + ethnic_group:parent_marital_status 11 134.597 4513.6 1488.5
## + ethnic_group:practice_sport 8 88.262 4560.0 1488.5
## + parent_marital_status:math_score 3 9.127 4639.1 1488.7
## + gender:parent_educ 5 39.289 4609.0 1488.8
## + ethnic_group:transport_means 4 23.187 4625.1 1488.9
## + parent_marital_status:transport_means 3 4.693 4643.5 1489.2
## + parent_marital_status:reading_score 3 3.852 4644.4 1489.3
## + practice_sport:wkly_study_hours 4 18.008 4630.2 1489.5
## + ethnic_group:reading_score 4 16.391 4631.9 1489.8
## - parent_educ:math_score 5 127.542 4775.8 1489.8
## - parent_marital_status:wkly_study_hours 6 156.016 4804.3 1491.3
## - math_score:reading_score 1 79.775 4728.0 1491.9
## + parent_marital_status:practice_sport 5 7.971 4640.3 1492.8
## - parent_educ:practice_sport 10 239.279 4887.5 1493.5
## + ethnic_group:parent_educ 20 230.416 4417.8 1493.8
## + parent_educ:wkly_study_hours 10 50.091 4598.2 1497.4
## - parent_educ:is_first_child 5 207.196 4855.4 1499.6
## + parent_educ:parent_marital_status 15 86.332 4561.9 1502.8
##
## Step: AIC=1481.84
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:is_first_child +
## gender:transport_means + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:math_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:transport_means 1 0.105 4648.4 1479.8
## - is_first_child:reading_score 1 0.248 4648.6 1479.9
## - gender:transport_means 1 0.334 4648.6 1479.9
## - gender:is_first_child 1 0.816 4649.1 1479.9
## - test_prep:reading_score 1 0.888 4649.2 1480.0
## - test_prep:math_score 1 1.367 4649.7 1480.0
## - lunch_type:test_prep 1 1.924 4650.2 1480.1
## - is_first_child:math_score 1 2.427 4650.7 1480.2
## - lunch_type:is_first_child 1 2.821 4651.1 1480.2
## - transport_means:reading_score 1 2.843 4651.2 1480.2
## - wkly_study_hours:reading_score 2 19.679 4668.0 1480.3
## - gender:lunch_type 1 4.303 4652.6 1480.4
## - transport_means:math_score 1 4.724 4653.0 1480.4
## - ethnic_group:wkly_study_hours 8 118.980 4767.3 1480.8
## - lunch_type:reading_score 1 8.703 4657.0 1480.9
## - test_prep:wkly_study_hours 2 25.175 4673.5 1481.0
## - transport_means:wkly_study_hours 2 25.220 4673.5 1481.0
## - lunch_type:math_score 1 10.455 4658.8 1481.2
## - test_prep:is_first_child 1 14.822 4663.1 1481.7
## - test_prep:transport_means 1 15.259 4663.6 1481.8
## <none> 4648.3 1481.8
## - gender:math_score 1 15.842 4664.2 1481.8
## - ethnic_group:lunch_type 4 67.486 4715.8 1482.3
## - practice_sport:math_score 2 37.911 4686.2 1482.6
## - practice_sport:is_first_child 2 38.084 4686.4 1482.7
## - test_prep:practice_sport 2 40.531 4688.8 1483.0
## - lunch_type:parent_marital_status 3 57.389 4705.7 1483.1
## - ethnic_group:test_prep 4 78.008 4726.3 1483.7
## - ethnic_group:is_first_child 4 78.672 4727.0 1483.7
## - test_prep:parent_marital_status 3 62.798 4711.1 1483.8
## - practice_sport:reading_score 2 47.031 4695.3 1483.8
## - parent_educ:reading_score 5 95.200 4743.5 1483.8
## + gender:test_prep 1 0.074 4648.2 1483.8
## + lunch_type:transport_means 1 0.029 4648.3 1483.8
## + parent_educ:test_prep 5 62.588 4585.7 1483.8
## - parent_educ:lunch_type 5 98.913 4747.2 1484.3
## - gender:ethnic_group 4 83.877 4732.2 1484.4
## - ethnic_group:math_score 4 83.975 4732.3 1484.4
## - gender:reading_score 1 36.167 4684.5 1484.4
## - parent_educ:transport_means 5 102.675 4751.0 1484.7
## + lunch_type:wkly_study_hours 2 7.492 4640.8 1484.9
## + gender:wkly_study_hours 2 6.490 4641.8 1485.0
## + wkly_study_hours:math_score 2 6.246 4642.1 1485.0
## + lunch_type:practice_sport 2 4.061 4644.3 1485.3
## + practice_sport:transport_means 2 3.983 4644.3 1485.3
## + is_first_child:wkly_study_hours 2 3.636 4644.7 1485.4
## + parent_marital_status:is_first_child 3 16.723 4631.6 1485.7
## + gender:practice_sport 2 0.699 4647.6 1485.8
## + gender:parent_marital_status 3 11.013 4637.3 1486.4
## + ethnic_group:practice_sport 8 88.113 4560.2 1486.5
## + ethnic_group:parent_marital_status 11 134.041 4514.3 1486.6
## + parent_marital_status:math_score 3 8.879 4639.4 1486.7
## + gender:parent_educ 5 39.291 4609.0 1486.8
## + ethnic_group:transport_means 4 23.252 4625.1 1486.9
## + parent_marital_status:transport_means 3 4.720 4643.6 1487.2
## + parent_marital_status:reading_score 3 3.755 4644.6 1487.4
## + practice_sport:wkly_study_hours 4 18.033 4630.3 1487.5
## + ethnic_group:reading_score 4 16.374 4631.9 1487.8
## - parent_educ:math_score 5 127.698 4776.0 1487.8
## - parent_marital_status:wkly_study_hours 6 156.389 4804.7 1489.4
## - math_score:reading_score 1 79.768 4728.1 1489.9
## + parent_marital_status:practice_sport 5 7.992 4640.3 1490.8
## - parent_educ:practice_sport 10 239.270 4887.6 1491.5
## + ethnic_group:parent_educ 20 230.488 4417.8 1491.8
## + parent_educ:wkly_study_hours 10 50.163 4598.2 1495.4
## - parent_educ:is_first_child 5 207.139 4855.5 1497.6
## + parent_educ:parent_marital_status 15 86.357 4562.0 1500.8
##
## Step: AIC=1479.85
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:is_first_child +
## gender:transport_means + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:reading_score 1 0.239 4648.7 1477.9
## - gender:transport_means 1 0.341 4648.8 1477.9
## - gender:is_first_child 1 0.808 4649.2 1478.0
## - test_prep:reading_score 1 0.896 4649.3 1478.0
## - test_prep:math_score 1 1.374 4649.8 1478.0
## - lunch_type:test_prep 1 1.885 4650.3 1478.1
## - is_first_child:math_score 1 2.375 4650.8 1478.2
## - transport_means:reading_score 1 2.818 4651.2 1478.2
## - lunch_type:is_first_child 1 2.829 4651.2 1478.2
## - wkly_study_hours:reading_score 2 19.628 4668.0 1478.3
## - gender:lunch_type 1 4.406 4652.8 1478.4
## - transport_means:math_score 1 4.780 4653.2 1478.5
## - ethnic_group:wkly_study_hours 8 119.009 4767.4 1478.8
## - lunch_type:reading_score 1 8.777 4657.2 1479.0
## - test_prep:wkly_study_hours 2 25.107 4673.5 1479.0
## - transport_means:wkly_study_hours 2 25.213 4673.6 1479.0
## - lunch_type:math_score 1 10.512 4658.9 1479.2
## - test_prep:is_first_child 1 14.729 4663.1 1479.7
## - test_prep:transport_means 1 15.162 4663.6 1479.8
## - gender:math_score 1 15.772 4664.2 1479.8
## <none> 4648.4 1479.8
## - ethnic_group:lunch_type 4 67.786 4716.2 1480.4
## - practice_sport:math_score 2 37.870 4686.3 1480.6
## - practice_sport:is_first_child 2 37.984 4686.4 1480.7
## - test_prep:practice_sport 2 40.488 4688.9 1481.0
## - lunch_type:parent_marital_status 3 57.457 4705.9 1481.1
## - ethnic_group:test_prep 4 77.905 4726.3 1481.7
## - test_prep:parent_marital_status 3 62.761 4711.2 1481.8
## - ethnic_group:is_first_child 4 78.859 4727.3 1481.8
## - practice_sport:reading_score 2 46.927 4695.3 1481.8
## - parent_educ:reading_score 5 95.095 4743.5 1481.8
## + is_first_child:transport_means 1 0.105 4648.3 1481.8
## + gender:test_prep 1 0.072 4648.3 1481.8
## + lunch_type:transport_means 1 0.025 4648.4 1481.8
## + parent_educ:test_prep 5 62.413 4586.0 1481.9
## - parent_educ:lunch_type 5 99.214 4747.6 1482.3
## - gender:reading_score 1 36.071 4684.5 1482.4
## - gender:ethnic_group 4 84.147 4732.6 1482.4
## - ethnic_group:math_score 4 84.614 4733.0 1482.5
## - parent_educ:transport_means 5 103.296 4751.7 1482.8
## + lunch_type:wkly_study_hours 2 7.370 4641.1 1482.9
## + gender:wkly_study_hours 2 6.427 4642.0 1483.0
## + wkly_study_hours:math_score 2 6.061 4642.4 1483.1
## + lunch_type:practice_sport 2 4.064 4644.4 1483.3
## + practice_sport:transport_means 2 3.922 4644.5 1483.4
## + is_first_child:wkly_study_hours 2 3.537 4644.9 1483.4
## + parent_marital_status:is_first_child 3 16.731 4631.7 1483.7
## + gender:practice_sport 2 0.682 4647.7 1483.8
## + gender:parent_marital_status 3 11.118 4637.3 1484.4
## + ethnic_group:parent_marital_status 11 133.866 4514.6 1484.6
## + ethnic_group:practice_sport 8 87.692 4560.7 1484.6
## + parent_marital_status:math_score 3 8.943 4639.5 1484.7
## + gender:parent_educ 5 39.248 4609.2 1484.8
## + ethnic_group:transport_means 4 23.356 4625.1 1484.9
## + parent_marital_status:transport_means 3 4.498 4643.9 1485.3
## + parent_marital_status:reading_score 3 3.834 4644.6 1485.4
## + practice_sport:wkly_study_hours 4 18.038 4630.4 1485.6
## + ethnic_group:reading_score 4 16.349 4632.1 1485.8
## - parent_educ:math_score 5 127.726 4776.1 1485.8
## - parent_marital_status:wkly_study_hours 6 156.336 4804.8 1487.4
## - math_score:reading_score 1 79.679 4728.1 1487.9
## + parent_marital_status:practice_sport 5 7.860 4640.6 1488.9
## - parent_educ:practice_sport 10 239.206 4887.6 1489.5
## + ethnic_group:parent_educ 20 230.555 4417.9 1489.8
## + parent_educ:wkly_study_hours 10 50.250 4598.2 1493.4
## - parent_educ:is_first_child 5 207.039 4855.5 1495.6
## + parent_educ:parent_marital_status 15 86.450 4562.0 1498.8
##
## Step: AIC=1477.88
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:is_first_child +
## gender:transport_means + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:wkly_study_hours + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + test_prep:reading_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 0.291 4648.9 1475.9
## - gender:is_first_child 1 0.616 4649.3 1476.0
## - test_prep:reading_score 1 0.788 4649.4 1476.0
## - test_prep:math_score 1 1.516 4650.2 1476.1
## - lunch_type:test_prep 1 1.836 4650.5 1476.1
## - transport_means:reading_score 1 2.671 4651.3 1476.2
## - lunch_type:is_first_child 1 2.960 4651.6 1476.3
## - wkly_study_hours:reading_score 2 19.472 4668.1 1476.3
## - gender:lunch_type 1 4.430 4653.1 1476.5
## - transport_means:math_score 1 4.981 4653.6 1476.5
## - is_first_child:math_score 1 6.092 4654.8 1476.7
## - ethnic_group:wkly_study_hours 8 118.881 4767.5 1476.8
## - lunch_type:reading_score 1 8.914 4657.6 1477.0
## - transport_means:wkly_study_hours 2 25.394 4674.1 1477.1
## - test_prep:wkly_study_hours 2 25.414 4674.1 1477.1
## - lunch_type:math_score 1 10.575 4659.2 1477.2
## - test_prep:transport_means 1 15.087 4663.7 1477.8
## <none> 4648.7 1477.9
## - gender:math_score 1 15.835 4664.5 1477.9
## - test_prep:is_first_child 1 15.907 4664.6 1477.9
## - ethnic_group:lunch_type 4 68.561 4717.2 1478.5
## - practice_sport:math_score 2 38.140 4686.8 1478.7
## - practice_sport:is_first_child 2 39.353 4688.0 1478.9
## - test_prep:practice_sport 2 40.528 4689.2 1479.0
## - lunch_type:parent_marital_status 3 57.349 4706.0 1479.1
## - ethnic_group:test_prep 4 77.673 4726.3 1479.7
## - test_prep:parent_marital_status 3 62.564 4711.2 1479.8
## - ethnic_group:is_first_child 4 78.625 4727.3 1479.8
## - parent_educ:reading_score 5 94.865 4743.5 1479.8
## - practice_sport:reading_score 2 47.016 4695.7 1479.8
## + is_first_child:reading_score 1 0.239 4648.4 1479.8
## + gender:test_prep 1 0.098 4648.6 1479.9
## + is_first_child:transport_means 1 0.096 4648.6 1479.9
## + lunch_type:transport_means 1 0.019 4648.6 1479.9
## + parent_educ:test_prep 5 62.585 4586.1 1479.9
## - parent_educ:lunch_type 5 99.061 4747.7 1480.3
## - gender:ethnic_group 4 83.910 4732.6 1480.4
## - gender:reading_score 1 36.548 4685.2 1480.5
## - ethnic_group:math_score 4 85.778 4734.4 1480.7
## + lunch_type:wkly_study_hours 2 7.309 4641.4 1481.0
## - parent_educ:transport_means 5 104.343 4753.0 1481.0
## + gender:wkly_study_hours 2 6.312 4642.3 1481.1
## + wkly_study_hours:math_score 2 6.065 4642.6 1481.1
## + lunch_type:practice_sport 2 4.039 4644.6 1481.4
## + practice_sport:transport_means 2 3.925 4644.7 1481.4
## + is_first_child:wkly_study_hours 2 3.341 4645.3 1481.5
## + gender:practice_sport 2 0.644 4648.0 1481.8
## + parent_marital_status:is_first_child 3 16.285 4632.4 1481.8
## + gender:parent_marital_status 3 11.032 4637.6 1482.5
## + ethnic_group:practice_sport 8 87.421 4561.2 1482.7
## + ethnic_group:parent_marital_status 11 133.249 4515.4 1482.7
## + parent_marital_status:math_score 3 8.830 4639.8 1482.8
## + gender:parent_educ 5 39.486 4609.2 1482.8
## + ethnic_group:transport_means 4 23.478 4625.2 1482.9
## + parent_marital_status:transport_means 3 4.449 4644.2 1483.3
## + parent_marital_status:reading_score 3 3.832 4644.8 1483.4
## + practice_sport:wkly_study_hours 4 18.024 4630.6 1483.6
## + ethnic_group:reading_score 4 16.267 4632.4 1483.8
## - parent_educ:math_score 5 127.558 4776.2 1483.9
## - parent_marital_status:wkly_study_hours 6 156.239 4804.9 1485.4
## - math_score:reading_score 1 79.440 4728.1 1485.9
## + parent_marital_status:practice_sport 5 7.766 4640.9 1486.9
## - parent_educ:practice_sport 10 239.245 4887.9 1487.5
## + ethnic_group:parent_educ 20 230.659 4418.0 1487.9
## + parent_educ:wkly_study_hours 10 50.240 4598.4 1491.5
## - parent_educ:is_first_child 5 207.310 4856.0 1493.6
## + parent_educ:parent_marital_status 15 86.311 4562.3 1496.8
##
## Step: AIC=1475.92
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:is_first_child +
## gender:math_score + gender:reading_score + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 0.646 4649.6 1474.0
## - test_prep:reading_score 1 0.807 4649.8 1474.0
## - test_prep:math_score 1 1.476 4650.4 1474.1
## - lunch_type:test_prep 1 1.879 4650.8 1474.2
## - lunch_type:is_first_child 1 2.904 4651.9 1474.3
## - transport_means:reading_score 1 2.960 4651.9 1474.3
## - wkly_study_hours:reading_score 2 19.352 4668.3 1474.4
## - gender:lunch_type 1 4.450 4653.4 1474.5
## - is_first_child:math_score 1 6.378 4655.3 1474.7
## - ethnic_group:wkly_study_hours 8 118.989 4767.9 1474.8
## - lunch_type:reading_score 1 9.043 4658.0 1475.1
## - test_prep:wkly_study_hours 2 25.201 4674.2 1475.1
## - transport_means:wkly_study_hours 2 25.505 4674.5 1475.2
## - lunch_type:math_score 1 10.853 4659.8 1475.3
## - transport_means:math_score 1 12.281 4661.2 1475.5
## - test_prep:transport_means 1 14.801 4663.8 1475.8
## <none> 4648.9 1475.9
## - test_prep:is_first_child 1 15.910 4664.9 1475.9
## - gender:math_score 1 15.936 4664.9 1475.9
## - ethnic_group:lunch_type 4 68.891 4717.8 1476.6
## - practice_sport:math_score 2 38.086 4687.0 1476.7
## - practice_sport:is_first_child 2 39.239 4688.2 1476.9
## - test_prep:practice_sport 2 40.712 4689.7 1477.1
## - lunch_type:parent_marital_status 3 57.363 4706.3 1477.2
## - ethnic_group:test_prep 4 77.461 4726.4 1477.7
## - ethnic_group:is_first_child 4 78.382 4727.3 1477.8
## - test_prep:parent_marital_status 3 62.498 4711.4 1477.8
## - practice_sport:reading_score 2 47.129 4696.1 1477.9
## + gender:transport_means 1 0.291 4648.7 1477.9
## + is_first_child:reading_score 1 0.189 4648.8 1477.9
## + is_first_child:transport_means 1 0.103 4648.8 1477.9
## + gender:test_prep 1 0.055 4648.9 1477.9
## + lunch_type:transport_means 1 0.005 4648.9 1477.9
## + parent_educ:test_prep 5 62.168 4586.8 1478.0
## - parent_educ:reading_score 5 96.004 4745.0 1478.0
## - parent_educ:lunch_type 5 100.222 4749.2 1478.5
## - gender:ethnic_group 4 84.208 4733.2 1478.5
## - gender:reading_score 1 36.455 4685.4 1478.5
## - ethnic_group:math_score 4 85.739 4734.7 1478.7
## + lunch_type:wkly_study_hours 2 7.280 4641.7 1479.0
## - parent_educ:transport_means 5 104.521 4753.5 1479.0
## + gender:wkly_study_hours 2 6.387 4642.6 1479.1
## + wkly_study_hours:math_score 2 6.181 4642.8 1479.1
## + lunch_type:practice_sport 2 4.039 4644.9 1479.4
## + practice_sport:transport_means 2 3.942 4645.0 1479.4
## + is_first_child:wkly_study_hours 2 3.360 4645.6 1479.5
## + parent_marital_status:is_first_child 3 16.452 4632.5 1479.8
## + gender:practice_sport 2 0.676 4648.3 1479.8
## + gender:parent_marital_status 3 10.918 4638.0 1480.5
## + ethnic_group:practice_sport 8 87.642 4561.3 1480.7
## + ethnic_group:parent_marital_status 11 133.271 4515.7 1480.8
## + parent_marital_status:math_score 3 8.776 4640.2 1480.8
## + gender:parent_educ 5 39.681 4609.3 1480.9
## + ethnic_group:transport_means 4 23.429 4625.5 1480.9
## + parent_marital_status:transport_means 3 4.357 4644.6 1481.4
## + parent_marital_status:reading_score 3 3.820 4645.1 1481.4
## + practice_sport:wkly_study_hours 4 17.824 4631.1 1481.7
## + ethnic_group:reading_score 4 16.110 4632.8 1481.9
## - parent_educ:math_score 5 128.216 4777.2 1482.0
## - parent_marital_status:wkly_study_hours 6 156.162 4805.1 1483.4
## - math_score:reading_score 1 79.598 4728.5 1483.9
## + parent_marital_status:practice_sport 5 7.580 4641.4 1485.0
## - parent_educ:practice_sport 10 239.461 4888.4 1485.5
## + ethnic_group:parent_educ 20 230.829 4418.1 1485.9
## + parent_educ:wkly_study_hours 10 50.235 4598.7 1489.5
## - parent_educ:is_first_child 5 207.115 4856.1 1491.6
## + parent_educ:parent_marital_status 15 86.331 4562.6 1494.9
##
## Step: AIC=1474
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + test_prep:reading_score +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## wkly_study_hours:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:reading_score 1 0.973 4650.6 1472.1
## - test_prep:math_score 1 1.342 4650.9 1472.2
## - lunch_type:test_prep 1 1.709 4651.3 1472.2
## - transport_means:reading_score 1 2.844 4652.4 1472.4
## - lunch_type:is_first_child 1 3.027 4652.6 1472.4
## - wkly_study_hours:reading_score 2 19.293 4668.9 1472.5
## - gender:lunch_type 1 4.223 4653.8 1472.5
## - is_first_child:math_score 1 5.825 4655.4 1472.7
## - ethnic_group:wkly_study_hours 8 118.653 4768.2 1472.9
## - lunch_type:reading_score 1 8.657 4658.3 1473.1
## - test_prep:wkly_study_hours 2 25.266 4674.9 1473.2
## - transport_means:wkly_study_hours 2 25.356 4675.0 1473.2
## - lunch_type:math_score 1 10.484 4660.1 1473.3
## - transport_means:math_score 1 12.091 4661.7 1473.5
## - test_prep:transport_means 1 14.727 4664.3 1473.9
## <none> 4649.6 1474.0
## - gender:math_score 1 16.218 4665.8 1474.1
## - test_prep:is_first_child 1 16.668 4666.3 1474.1
## - ethnic_group:lunch_type 4 68.692 4718.3 1474.7
## - practice_sport:math_score 2 37.950 4687.5 1474.8
## - practice_sport:is_first_child 2 38.724 4688.3 1474.9
## - test_prep:practice_sport 2 40.252 4689.8 1475.1
## - lunch_type:parent_marital_status 3 56.994 4706.6 1475.2
## - ethnic_group:test_prep 4 76.913 4726.5 1475.7
## - ethnic_group:is_first_child 4 77.737 4727.3 1475.8
## - test_prep:parent_marital_status 3 62.182 4711.8 1475.8
## - practice_sport:reading_score 2 46.689 4696.3 1475.9
## + gender:is_first_child 1 0.646 4648.9 1475.9
## + gender:transport_means 1 0.321 4649.3 1476.0
## + is_first_child:transport_means 1 0.108 4649.5 1476.0
## + is_first_child:reading_score 1 0.071 4649.5 1476.0
## + gender:test_prep 1 0.062 4649.5 1476.0
## + lunch_type:transport_means 1 0.001 4649.6 1476.0
## - parent_educ:reading_score 5 95.632 4745.2 1476.0
## + parent_educ:test_prep 5 62.135 4587.5 1476.1
## - gender:ethnic_group 4 83.567 4733.2 1476.5
## - parent_educ:lunch_type 5 100.511 4750.1 1476.6
## - gender:reading_score 1 37.103 4686.7 1476.7
## - ethnic_group:math_score 4 85.598 4735.2 1476.8
## + lunch_type:wkly_study_hours 2 7.206 4642.4 1477.1
## + gender:wkly_study_hours 2 6.314 4643.3 1477.2
## + wkly_study_hours:math_score 2 6.115 4643.5 1477.2
## - parent_educ:transport_means 5 105.414 4755.0 1477.2
## + lunch_type:practice_sport 2 4.449 4645.1 1477.4
## + practice_sport:transport_means 2 4.128 4645.5 1477.5
## + is_first_child:wkly_study_hours 2 3.022 4646.6 1477.6
## + parent_marital_status:is_first_child 3 16.767 4632.8 1477.9
## + gender:practice_sport 2 0.568 4649.0 1477.9
## + gender:parent_marital_status 3 10.664 4638.9 1478.7
## + ethnic_group:practice_sport 8 87.418 4562.2 1478.8
## + parent_marital_status:math_score 3 8.633 4641.0 1478.9
## + gender:parent_educ 5 39.096 4610.5 1479.0
## + ethnic_group:transport_means 4 23.351 4626.2 1479.0
## + ethnic_group:parent_marital_status 11 131.230 4518.4 1479.1
## + parent_marital_status:transport_means 3 4.615 4645.0 1479.4
## + parent_marital_status:reading_score 3 3.718 4645.9 1479.5
## + practice_sport:wkly_study_hours 4 17.860 4631.7 1479.7
## + ethnic_group:reading_score 4 16.424 4633.2 1479.9
## - parent_educ:math_score 5 128.151 4777.7 1480.0
## - parent_marital_status:wkly_study_hours 6 155.564 4805.2 1481.4
## - math_score:reading_score 1 80.084 4729.7 1482.1
## + parent_marital_status:practice_sport 5 7.476 4642.1 1483.0
## - parent_educ:practice_sport 10 239.926 4889.5 1483.7
## + ethnic_group:parent_educ 20 228.660 4420.9 1484.2
## + parent_educ:wkly_study_hours 10 49.429 4600.2 1487.7
## - parent_educ:is_first_child 5 206.473 4856.1 1489.6
## + parent_educ:parent_marital_status 15 86.330 4563.3 1493.0
##
## Step: AIC=1472.13
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 2.058 4652.6 1470.4
## - lunch_type:is_first_child 1 3.240 4653.8 1470.5
## - wkly_study_hours:reading_score 2 19.153 4669.7 1470.5
## - transport_means:reading_score 1 3.354 4653.9 1470.5
## - gender:lunch_type 1 4.125 4654.7 1470.7
## - is_first_child:math_score 1 6.076 4656.6 1470.9
## - ethnic_group:wkly_study_hours 8 119.207 4769.8 1471.1
## - test_prep:math_score 1 8.298 4658.9 1471.2
## - lunch_type:reading_score 1 8.325 4658.9 1471.2
## - transport_means:wkly_study_hours 2 24.609 4675.2 1471.2
## - test_prep:wkly_study_hours 2 25.606 4676.2 1471.4
## - lunch_type:math_score 1 10.301 4660.9 1471.4
## - transport_means:math_score 1 11.644 4662.2 1471.6
## - test_prep:transport_means 1 15.143 4665.7 1472.0
## <none> 4650.6 1472.1
## - test_prep:is_first_child 1 16.716 4667.3 1472.2
## - gender:math_score 1 16.980 4667.5 1472.3
## - ethnic_group:lunch_type 4 67.973 4718.5 1472.7
## - practice_sport:math_score 2 38.500 4689.1 1473.0
## - practice_sport:is_first_child 2 38.679 4689.2 1473.0
## - test_prep:practice_sport 2 41.371 4691.9 1473.3
## - lunch_type:parent_marital_status 3 58.052 4708.6 1473.5
## - ethnic_group:test_prep 4 76.260 4726.8 1473.7
## - test_prep:parent_marital_status 3 61.566 4712.1 1473.9
## - ethnic_group:is_first_child 4 78.359 4728.9 1474.0
## + test_prep:reading_score 1 0.973 4649.6 1474.0
## + gender:is_first_child 1 0.812 4649.8 1474.0
## + gender:test_prep 1 0.770 4649.8 1474.0
## + parent_educ:test_prep 5 63.038 4587.5 1474.1
## + gender:transport_means 1 0.347 4650.2 1474.1
## + is_first_child:reading_score 1 0.186 4650.4 1474.1
## + is_first_child:transport_means 1 0.120 4650.4 1474.1
## - practice_sport:reading_score 2 47.440 4698.0 1474.1
## + lunch_type:transport_means 1 0.000 4650.6 1474.1
## - parent_educ:reading_score 5 95.802 4746.4 1474.2
## - gender:ethnic_group 4 82.715 4733.3 1474.5
## - ethnic_group:math_score 4 85.462 4736.0 1474.9
## - parent_educ:lunch_type 5 102.644 4753.2 1475.0
## - gender:reading_score 1 38.805 4689.4 1475.0
## + lunch_type:wkly_study_hours 2 7.499 4643.1 1475.2
## + wkly_study_hours:math_score 2 6.215 4644.4 1475.3
## + gender:wkly_study_hours 2 6.004 4644.6 1475.4
## - parent_educ:transport_means 5 106.330 4756.9 1475.5
## + lunch_type:practice_sport 2 4.449 4646.1 1475.6
## + practice_sport:transport_means 2 4.078 4646.5 1475.6
## + is_first_child:wkly_study_hours 2 3.049 4647.5 1475.7
## + parent_marital_status:is_first_child 3 17.169 4633.4 1475.9
## + gender:practice_sport 2 0.522 4650.0 1476.1
## + gender:parent_marital_status 3 10.880 4639.7 1476.8
## + ethnic_group:practice_sport 8 88.117 4562.5 1476.8
## + parent_marital_status:math_score 3 8.755 4641.8 1477.0
## + gender:parent_educ 5 39.051 4611.5 1477.2
## + ethnic_group:parent_marital_status 11 131.877 4518.7 1477.2
## + ethnic_group:transport_means 4 23.290 4627.3 1477.2
## + parent_marital_status:transport_means 3 4.664 4645.9 1477.5
## + parent_marital_status:reading_score 3 3.790 4646.8 1477.7
## + practice_sport:wkly_study_hours 4 17.801 4632.8 1477.9
## + ethnic_group:reading_score 4 16.558 4634.0 1478.0
## - parent_educ:math_score 5 129.498 4780.1 1478.3
## - parent_marital_status:wkly_study_hours 6 157.100 4807.7 1479.7
## - math_score:reading_score 1 81.119 4731.7 1480.3
## + parent_marital_status:practice_sport 5 7.530 4643.0 1481.2
## - parent_educ:practice_sport 10 239.745 4890.3 1481.8
## + ethnic_group:parent_educ 20 228.646 4421.9 1482.4
## + parent_educ:wkly_study_hours 10 48.983 4601.6 1485.9
## - parent_educ:is_first_child 5 208.569 4859.1 1488.0
## + parent_educ:parent_marital_status 15 85.247 4565.3 1491.2
##
## Step: AIC=1470.39
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + wkly_study_hours:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - wkly_study_hours:reading_score 2 18.717 4671.3 1468.8
## - lunch_type:is_first_child 1 3.006 4655.6 1468.8
## - transport_means:reading_score 1 3.532 4656.2 1468.8
## - gender:lunch_type 1 3.703 4656.3 1468.9
## - ethnic_group:wkly_study_hours 8 117.155 4769.8 1469.1
## - is_first_child:math_score 1 5.962 4658.6 1469.1
## - test_prep:math_score 1 6.303 4658.9 1469.2
## - lunch_type:reading_score 1 7.384 4660.0 1469.3
## - test_prep:wkly_study_hours 2 24.822 4677.4 1469.5
## - transport_means:wkly_study_hours 2 25.450 4678.1 1469.6
## - lunch_type:math_score 1 10.247 4662.9 1469.7
## - transport_means:math_score 1 11.271 4663.9 1469.8
## - test_prep:transport_means 1 15.609 4668.2 1470.4
## <none> 4652.6 1470.4
## - test_prep:is_first_child 1 16.899 4669.5 1470.5
## - gender:math_score 1 17.132 4669.8 1470.6
## - ethnic_group:lunch_type 4 67.657 4720.3 1470.9
## - practice_sport:is_first_child 2 37.719 4690.3 1471.2
## - practice_sport:math_score 2 38.098 4690.7 1471.2
## - lunch_type:parent_marital_status 3 56.250 4708.9 1471.5
## - test_prep:practice_sport 2 40.697 4693.3 1471.5
## - ethnic_group:test_prep 4 75.720 4728.3 1471.9
## - test_prep:parent_marital_status 3 60.499 4713.1 1472.0
## - ethnic_group:is_first_child 4 77.019 4729.6 1472.1
## + lunch_type:test_prep 1 2.058 4650.6 1472.1
## + test_prep:reading_score 1 1.323 4651.3 1472.2
## + parent_educ:test_prep 5 63.592 4589.0 1472.3
## + gender:test_prep 1 0.776 4651.9 1472.3
## + gender:is_first_child 1 0.630 4652.0 1472.3
## - practice_sport:reading_score 2 47.020 4699.6 1472.3
## + gender:transport_means 1 0.397 4652.2 1472.3
## + is_first_child:reading_score 1 0.173 4652.5 1472.4
## - parent_educ:reading_score 5 95.465 4748.1 1472.4
## + is_first_child:transport_means 1 0.080 4652.5 1472.4
## + lunch_type:transport_means 1 0.036 4652.6 1472.4
## - gender:ethnic_group 4 82.358 4735.0 1472.7
## - parent_educ:lunch_type 5 100.671 4753.3 1473.0
## - ethnic_group:math_score 4 85.072 4737.7 1473.1
## - gender:reading_score 1 38.860 4691.5 1473.3
## + lunch_type:wkly_study_hours 2 8.197 4644.4 1473.3
## - parent_educ:transport_means 5 105.075 4757.7 1473.6
## + wkly_study_hours:math_score 2 5.997 4646.6 1473.6
## + gender:wkly_study_hours 2 5.745 4646.9 1473.7
## + lunch_type:practice_sport 2 4.805 4647.8 1473.8
## + practice_sport:transport_means 2 3.484 4649.1 1474.0
## + is_first_child:wkly_study_hours 2 3.361 4649.3 1474.0
## + parent_marital_status:is_first_child 3 17.183 4635.4 1474.2
## + gender:practice_sport 2 0.326 4652.3 1474.3
## + ethnic_group:practice_sport 8 89.413 4563.2 1474.9
## + gender:parent_marital_status 3 10.590 4642.0 1475.0
## + parent_marital_status:math_score 3 9.163 4643.5 1475.2
## + ethnic_group:transport_means 4 23.982 4628.6 1475.3
## + ethnic_group:parent_marital_status 11 132.395 4520.2 1475.4
## + gender:parent_educ 5 38.868 4613.8 1475.4
## + parent_marital_status:transport_means 3 4.658 4648.0 1475.8
## + parent_marital_status:reading_score 3 3.783 4648.8 1475.9
## + practice_sport:wkly_study_hours 4 17.986 4634.6 1476.1
## + ethnic_group:reading_score 4 16.713 4635.9 1476.3
## - parent_educ:math_score 5 129.320 4781.9 1476.6
## - parent_marital_status:wkly_study_hours 6 156.063 4808.7 1477.8
## - math_score:reading_score 1 87.153 4739.8 1479.3
## + parent_marital_status:practice_sport 5 7.708 4644.9 1479.4
## - parent_educ:practice_sport 10 239.948 4892.6 1480.1
## + ethnic_group:parent_educ 20 228.813 4423.8 1480.6
## + parent_educ:wkly_study_hours 10 49.974 4602.7 1484.0
## - parent_educ:is_first_child 5 206.810 4859.4 1486.0
## + parent_educ:parent_marital_status 15 85.389 4567.2 1489.5
##
## Step: AIC=1468.76
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:wkly_study_hours +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 110.675 4782.0 1466.6
## - gender:lunch_type 1 3.092 4674.4 1467.2
## - lunch_type:is_first_child 1 3.564 4674.9 1467.2
## - transport_means:reading_score 1 3.971 4675.3 1467.3
## - transport_means:wkly_study_hours 2 21.001 4692.3 1467.4
## - is_first_child:math_score 1 5.419 4676.8 1467.4
## - lunch_type:reading_score 1 5.991 4677.3 1467.5
## - test_prep:wkly_study_hours 2 22.692 4694.0 1467.6
## - test_prep:math_score 1 6.986 4678.3 1467.6
## - lunch_type:math_score 1 8.903 4680.2 1467.9
## - transport_means:math_score 1 9.271 4680.6 1467.9
## - ethnic_group:lunch_type 4 60.942 4732.3 1468.4
## - test_prep:is_first_child 1 14.759 4686.1 1468.6
## <none> 4671.3 1468.8
## - gender:math_score 1 17.474 4688.8 1469.0
## - practice_sport:is_first_child 2 35.441 4706.8 1469.2
## - test_prep:transport_means 1 19.860 4691.2 1469.3
## - practice_sport:math_score 2 38.079 4709.4 1469.5
## - test_prep:practice_sport 2 38.936 4710.3 1469.7
## - ethnic_group:test_prep 4 71.096 4742.4 1469.7
## - test_prep:parent_marital_status 3 56.201 4727.5 1469.8
## - lunch_type:parent_marital_status 3 57.876 4729.2 1470.0
## - ethnic_group:is_first_child 4 74.560 4745.9 1470.1
## + parent_educ:test_prep 5 67.127 4604.2 1470.2
## + wkly_study_hours:reading_score 2 18.717 4652.6 1470.4
## + lunch_type:test_prep 1 1.623 4669.7 1470.5
## + test_prep:reading_score 1 1.127 4670.2 1470.6
## + gender:test_prep 1 0.612 4670.7 1470.7
## + gender:is_first_child 1 0.578 4670.8 1470.7
## + is_first_child:reading_score 1 0.257 4671.1 1470.7
## + gender:transport_means 1 0.249 4671.1 1470.7
## + lunch_type:transport_means 1 0.244 4671.1 1470.7
## + is_first_child:transport_means 1 0.039 4671.3 1470.8
## - practice_sport:reading_score 2 49.337 4720.7 1471.0
## - parent_educ:reading_score 5 97.784 4769.1 1471.0
## - parent_educ:lunch_type 5 99.831 4771.2 1471.2
## - gender:ethnic_group 4 84.193 4755.5 1471.3
## + lunch_type:wkly_study_hours 2 11.270 4660.1 1471.3
## + gender:wkly_study_hours 2 9.260 4662.1 1471.6
## - gender:reading_score 1 39.085 4710.4 1471.7
## + wkly_study_hours:math_score 2 6.049 4665.3 1472.0
## - parent_educ:transport_means 5 106.345 4777.7 1472.0
## + lunch_type:practice_sport 2 5.368 4666.0 1472.1
## - ethnic_group:math_score 4 92.617 4764.0 1472.3
## + is_first_child:wkly_study_hours 2 2.954 4668.4 1472.4
## + parent_marital_status:is_first_child 3 18.631 4652.7 1472.4
## + practice_sport:transport_means 2 2.781 4668.6 1472.4
## + gender:practice_sport 2 0.692 4670.7 1472.7
## + gender:parent_marital_status 3 12.675 4658.7 1473.2
## + ethnic_group:practice_sport 8 90.916 4580.4 1473.2
## + ethnic_group:parent_marital_status 11 135.175 4536.2 1473.4
## + parent_marital_status:math_score 3 10.154 4661.2 1473.5
## + gender:parent_educ 5 39.098 4632.2 1473.8
## + parent_marital_status:transport_means 3 6.176 4665.2 1474.0
## + parent_marital_status:reading_score 3 4.863 4666.5 1474.1
## + ethnic_group:transport_means 4 19.875 4651.5 1474.2
## + ethnic_group:reading_score 4 18.726 4652.6 1474.4
## + practice_sport:wkly_study_hours 4 16.985 4654.4 1474.6
## - parent_educ:math_score 5 127.829 4799.2 1474.7
## - math_score:reading_score 1 78.623 4750.0 1476.6
## - parent_marital_status:wkly_study_hours 6 166.681 4838.0 1477.4
## + parent_marital_status:practice_sport 5 8.333 4663.0 1477.7
## + ethnic_group:parent_educ 20 231.018 4440.3 1478.8
## - parent_educ:practice_sport 10 250.043 4921.4 1479.5
## + parent_educ:wkly_study_hours 10 49.669 4621.7 1482.5
## - parent_educ:is_first_child 5 208.635 4880.0 1484.5
## + parent_educ:parent_marital_status 15 84.066 4587.3 1488.0
##
## Step: AIC=1466.57
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:math_score + parent_educ:lunch_type +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:math_score +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:math_score 1 1.182 4783.2 1464.7
## - gender:lunch_type 1 1.928 4783.9 1464.8
## - lunch_type:reading_score 1 4.088 4786.1 1465.1
## - transport_means:wkly_study_hours 2 20.969 4803.0 1465.2
## - transport_means:reading_score 1 5.140 4787.2 1465.2
## - lunch_type:math_score 1 5.171 4787.2 1465.2
## - transport_means:math_score 1 5.903 4787.9 1465.3
## - lunch_type:is_first_child 1 7.970 4790.0 1465.5
## - test_prep:math_score 1 8.701 4790.7 1465.6
## - test_prep:is_first_child 1 12.308 4794.3 1466.1
## - test_prep:wkly_study_hours 2 29.311 4811.3 1466.2
## - test_prep:parent_marital_status 3 46.188 4828.2 1466.2
## - test_prep:transport_means 1 16.016 4798.0 1466.5
## <none> 4782.0 1466.6
## - ethnic_group:lunch_type 4 65.689 4847.7 1466.6
## - practice_sport:math_score 2 34.438 4816.5 1466.8
## - gender:math_score 1 19.755 4801.8 1467.0
## - ethnic_group:is_first_child 4 69.381 4851.4 1467.1
## - lunch_type:parent_marital_status 3 54.647 4836.7 1467.3
## - test_prep:practice_sport 2 39.005 4821.0 1467.4
## - practice_sport:is_first_child 2 40.026 4822.0 1467.5
## - practice_sport:reading_score 2 42.005 4824.0 1467.7
## - parent_educ:reading_score 5 93.930 4875.9 1468.0
## + parent_educ:test_prep 5 68.036 4714.0 1468.1
## - gender:ethnic_group 4 79.023 4861.0 1468.2
## + test_prep:reading_score 1 1.285 4780.7 1468.4
## + is_first_child:reading_score 1 1.024 4781.0 1468.5
## + gender:is_first_child 1 0.492 4781.5 1468.5
## + gender:test_prep 1 0.419 4781.6 1468.5
## + gender:transport_means 1 0.362 4781.7 1468.5
## + is_first_child:transport_means 1 0.155 4781.9 1468.5
## + lunch_type:transport_means 1 0.096 4781.9 1468.6
## + lunch_type:test_prep 1 0.008 4782.0 1468.6
## + ethnic_group:wkly_study_hours 8 110.675 4671.3 1468.8
## + wkly_study_hours:reading_score 2 12.237 4769.8 1469.1
## - parent_educ:lunch_type 5 103.689 4885.7 1469.2
## + lunch_type:wkly_study_hours 2 10.874 4771.1 1469.2
## - ethnic_group:math_score 4 89.968 4872.0 1469.6
## + lunch_type:practice_sport 2 7.998 4774.0 1469.6
## - gender:reading_score 1 40.909 4822.9 1469.6
## + gender:wkly_study_hours 2 6.097 4775.9 1469.8
## - ethnic_group:test_prep 4 92.510 4874.5 1469.9
## + practice_sport:transport_means 2 3.723 4778.3 1470.1
## + wkly_study_hours:math_score 2 2.164 4779.9 1470.3
## + is_first_child:wkly_study_hours 2 1.462 4780.6 1470.4
## + gender:parent_marital_status 3 17.134 4764.9 1470.5
## + gender:practice_sport 2 0.532 4781.5 1470.5
## + parent_marital_status:is_first_child 3 14.764 4767.3 1470.8
## + parent_marital_status:math_score 3 10.602 4771.4 1471.3
## - parent_educ:transport_means 5 120.741 4902.8 1471.3
## - parent_educ:math_score 5 121.030 4903.0 1471.3
## + parent_marital_status:transport_means 3 9.757 4772.3 1471.4
## + ethnic_group:reading_score 4 25.436 4756.6 1471.4
## + parent_marital_status:reading_score 3 5.725 4776.3 1471.9
## + ethnic_group:practice_sport 8 85.057 4697.0 1472.0
## + gender:parent_educ 5 35.964 4746.1 1472.1
## + ethnic_group:transport_means 4 17.989 4764.0 1472.3
## + ethnic_group:parent_marital_status 11 125.547 4656.5 1472.9
## + practice_sport:wkly_study_hours 4 6.691 4775.3 1473.8
## - parent_marital_status:wkly_study_hours 6 164.411 4946.4 1474.5
## - math_score:reading_score 1 84.761 4866.8 1474.9
## + parent_marital_status:practice_sport 5 4.190 4777.8 1476.1
## - parent_educ:practice_sport 10 260.322 5042.3 1477.8
## + ethnic_group:parent_educ 20 213.449 4568.6 1479.6
## - parent_educ:is_first_child 5 196.318 4978.3 1480.3
## + parent_educ:wkly_study_hours 10 35.027 4747.0 1482.2
## + parent_educ:parent_marital_status 15 95.972 4686.0 1484.6
##
## Step: AIC=1464.72
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:math_score +
## gender:reading_score + ethnic_group:lunch_type + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:math_score + parent_educ:lunch_type +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## lunch_type:math_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 1.941 4785.1 1463.0
## - lunch_type:reading_score 1 3.941 4787.1 1463.2
## - transport_means:reading_score 1 4.872 4788.1 1463.3
## - lunch_type:math_score 1 5.207 4788.4 1463.4
## - transport_means:wkly_study_hours 2 21.524 4804.7 1463.4
## - transport_means:math_score 1 5.990 4789.2 1463.5
## - test_prep:math_score 1 8.301 4791.5 1463.7
## - test_prep:is_first_child 1 11.399 4794.6 1464.1
## - lunch_type:is_first_child 1 12.411 4795.6 1464.2
## - test_prep:wkly_study_hours 2 29.413 4812.6 1464.3
## - test_prep:parent_marital_status 3 45.849 4829.1 1464.3
## - test_prep:transport_means 1 15.876 4799.1 1464.7
## <none> 4783.2 1464.7
## - ethnic_group:lunch_type 4 65.597 4848.8 1464.8
## - practice_sport:math_score 2 34.075 4817.3 1464.9
## - gender:math_score 1 19.288 4802.5 1465.1
## - ethnic_group:is_first_child 4 68.617 4851.8 1465.1
## - lunch_type:parent_marital_status 3 54.323 4837.5 1465.4
## - test_prep:practice_sport 2 39.983 4823.2 1465.6
## - practice_sport:is_first_child 2 40.111 4823.3 1465.7
## - practice_sport:reading_score 2 41.819 4825.0 1465.8
## - parent_educ:reading_score 5 92.914 4876.1 1466.1
## + parent_educ:test_prep 5 68.072 4715.1 1466.3
## - gender:ethnic_group 4 78.569 4861.8 1466.3
## + is_first_child:reading_score 1 2.187 4781.0 1466.5
## + test_prep:reading_score 1 1.395 4781.8 1466.5
## + is_first_child:math_score 1 1.182 4782.0 1466.6
## + gender:test_prep 1 0.483 4782.7 1466.7
## + gender:transport_means 1 0.467 4782.7 1466.7
## + gender:is_first_child 1 0.227 4783.0 1466.7
## + lunch_type:transport_means 1 0.116 4783.1 1466.7
## + is_first_child:transport_means 1 0.094 4783.1 1466.7
## + lunch_type:test_prep 1 0.008 4783.2 1466.7
## + wkly_study_hours:reading_score 2 12.031 4771.2 1467.2
## - parent_educ:lunch_type 5 102.967 4886.2 1467.3
## + lunch_type:wkly_study_hours 2 10.546 4772.7 1467.4
## + ethnic_group:wkly_study_hours 8 106.437 4676.8 1467.4
## - gender:reading_score 1 40.293 4823.5 1467.7
## + lunch_type:practice_sport 2 8.053 4775.1 1467.7
## - ethnic_group:math_score 4 90.566 4873.8 1467.8
## + gender:wkly_study_hours 2 6.321 4776.9 1467.9
## - ethnic_group:test_prep 4 93.047 4876.2 1468.1
## + practice_sport:transport_means 2 3.724 4779.5 1468.3
## + wkly_study_hours:math_score 2 2.008 4781.2 1468.5
## + is_first_child:wkly_study_hours 2 1.288 4781.9 1468.6
## + gender:parent_marital_status 3 17.165 4766.0 1468.6
## + gender:practice_sport 2 0.548 4782.7 1468.7
## + parent_marital_status:is_first_child 3 14.759 4768.4 1468.9
## - parent_educ:math_score 5 120.430 4903.6 1469.4
## - parent_educ:transport_means 5 120.842 4904.0 1469.4
## + parent_marital_status:math_score 3 10.264 4772.9 1469.5
## + parent_marital_status:transport_means 3 9.795 4773.4 1469.5
## + ethnic_group:reading_score 4 25.829 4757.4 1469.5
## + parent_marital_status:reading_score 3 5.389 4777.8 1470.0
## + ethnic_group:practice_sport 8 84.129 4699.1 1470.2
## + gender:parent_educ 5 36.031 4747.2 1470.3
## + ethnic_group:transport_means 4 18.379 4764.8 1470.5
## + ethnic_group:parent_marital_status 11 124.113 4659.1 1471.2
## + practice_sport:wkly_study_hours 4 7.001 4776.2 1471.8
## - parent_marital_status:wkly_study_hours 6 166.770 4950.0 1472.9
## - math_score:reading_score 1 91.806 4875.0 1473.9
## + parent_marital_status:practice_sport 5 4.360 4778.8 1474.2
## - parent_educ:practice_sport 10 260.127 5043.3 1476.0
## + ethnic_group:parent_educ 20 213.547 4569.7 1477.8
## - parent_educ:is_first_child 5 201.760 4985.0 1479.1
## + parent_educ:wkly_study_hours 10 35.100 4748.1 1480.4
## + parent_educ:parent_marital_status 15 95.698 4687.5 1482.8
##
## Step: AIC=1462.96
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + lunch_type:reading_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:reading_score 1 2.004 4787.1 1461.2
## - lunch_type:math_score 1 3.289 4788.4 1461.4
## - transport_means:wkly_study_hours 2 20.963 4806.1 1461.5
## - transport_means:math_score 1 5.331 4790.5 1461.6
## - transport_means:reading_score 1 5.335 4790.5 1461.6
## - test_prep:math_score 1 8.656 4793.8 1462.0
## - test_prep:is_first_child 1 11.840 4797.0 1462.4
## - test_prep:wkly_study_hours 2 28.959 4814.1 1462.5
## - lunch_type:is_first_child 1 14.019 4799.2 1462.7
## - test_prep:parent_marital_status 3 46.761 4831.9 1462.7
## - ethnic_group:lunch_type 4 64.686 4849.8 1462.9
## <none> 4785.1 1463.0
## - test_prep:transport_means 1 16.292 4801.4 1463.0
## - practice_sport:math_score 2 34.261 4819.4 1463.2
## - ethnic_group:is_first_child 4 70.509 4855.7 1463.6
## - lunch_type:parent_marital_status 3 54.080 4839.2 1463.6
## - gender:math_score 1 24.168 4809.3 1463.9
## - test_prep:practice_sport 2 41.462 4826.6 1464.0
## - practice_sport:is_first_child 2 41.876 4827.0 1464.1
## - practice_sport:reading_score 2 42.514 4827.7 1464.2
## - parent_educ:reading_score 5 93.442 4878.6 1464.4
## - gender:ethnic_group 4 77.856 4863.0 1464.5
## + parent_educ:test_prep 5 67.034 4718.1 1464.6
## + is_first_child:reading_score 1 2.051 4783.1 1464.7
## + gender:lunch_type 1 1.941 4783.2 1464.7
## + test_prep:reading_score 1 1.310 4783.8 1464.8
## + is_first_child:math_score 1 1.195 4783.9 1464.8
## + gender:test_prep 1 0.605 4784.5 1464.9
## + gender:transport_means 1 0.489 4784.7 1464.9
## + lunch_type:transport_means 1 0.170 4785.0 1464.9
## + is_first_child:transport_means 1 0.157 4785.0 1464.9
## + gender:is_first_child 1 0.146 4785.0 1464.9
## + lunch_type:test_prep 1 0.039 4785.1 1465.0
## + wkly_study_hours:reading_score 2 11.793 4773.3 1465.5
## + lunch_type:wkly_study_hours 2 10.195 4774.9 1465.7
## + ethnic_group:wkly_study_hours 8 105.288 4679.9 1465.8
## - parent_educ:lunch_type 5 106.440 4891.6 1465.9
## + lunch_type:practice_sport 2 8.207 4776.9 1465.9
## - ethnic_group:math_score 4 90.516 4875.7 1466.0
## + gender:wkly_study_hours 2 6.681 4778.5 1466.1
## - gender:reading_score 1 43.560 4828.7 1466.3
## - ethnic_group:test_prep 4 93.755 4878.9 1466.4
## + practice_sport:transport_means 2 3.823 4781.3 1466.5
## + wkly_study_hours:math_score 2 1.904 4783.2 1466.7
## + gender:parent_marital_status 3 17.636 4767.5 1466.8
## + is_first_child:wkly_study_hours 2 1.396 4783.7 1466.8
## + gender:practice_sport 2 0.777 4784.4 1466.9
## + parent_marital_status:is_first_child 3 15.015 4770.1 1467.1
## + parent_marital_status:math_score 3 10.405 4774.7 1467.7
## + parent_marital_status:transport_means 3 9.920 4775.2 1467.7
## + ethnic_group:reading_score 4 26.040 4759.1 1467.7
## - parent_educ:math_score 5 122.116 4907.3 1467.8
## - parent_educ:transport_means 5 123.053 4908.2 1467.9
## + parent_marital_status:reading_score 3 5.362 4779.8 1468.3
## + gender:parent_educ 5 36.902 4748.2 1468.4
## + ethnic_group:practice_sport 8 83.462 4701.7 1468.6
## + ethnic_group:transport_means 4 18.858 4766.3 1468.6
## + ethnic_group:parent_marital_status 11 124.997 4660.1 1469.3
## + practice_sport:wkly_study_hours 4 6.453 4778.7 1470.2
## - parent_marital_status:wkly_study_hours 6 168.047 4953.2 1471.3
## - math_score:reading_score 1 91.152 4876.3 1472.1
## + parent_marital_status:practice_sport 5 4.286 4780.9 1472.4
## - parent_educ:practice_sport 10 261.469 5046.6 1474.3
## + ethnic_group:parent_educ 20 213.656 4571.5 1476.0
## - parent_educ:is_first_child 5 200.856 4986.0 1477.2
## + parent_educ:wkly_study_hours 10 34.190 4751.0 1478.7
## + parent_educ:parent_marital_status 15 96.087 4689.1 1481.0
##
## Step: AIC=1461.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:math_score 1 1.298 4788.4 1459.4
## - transport_means:wkly_study_hours 2 20.461 4807.6 1459.7
## - transport_means:math_score 1 5.126 4792.3 1459.8
## - transport_means:reading_score 1 5.492 4792.6 1459.9
## - test_prep:math_score 1 8.260 4795.4 1460.2
## - test_prep:is_first_child 1 11.806 4799.0 1460.7
## - test_prep:wkly_study_hours 2 28.216 4815.4 1460.7
## - test_prep:parent_marital_status 3 47.274 4834.4 1461.0
## - ethnic_group:lunch_type 4 64.214 4851.4 1461.1
## - lunch_type:is_first_child 1 15.264 4802.4 1461.1
## <none> 4787.1 1461.2
## - test_prep:transport_means 1 16.638 4803.8 1461.2
## - practice_sport:math_score 2 35.631 4822.8 1461.6
## - lunch_type:parent_marital_status 3 54.208 4841.4 1461.8
## - ethnic_group:is_first_child 4 71.706 4858.9 1462.0
## - gender:math_score 1 22.652 4809.8 1462.0
## - practice_sport:is_first_child 2 40.687 4827.8 1462.2
## - test_prep:practice_sport 2 41.943 4829.1 1462.3
## - parent_educ:reading_score 5 92.753 4879.9 1462.5
## - practice_sport:reading_score 2 43.632 4830.8 1462.6
## - gender:ethnic_group 4 78.545 4865.7 1462.8
## + lunch_type:reading_score 1 2.004 4785.1 1463.0
## + is_first_child:reading_score 1 1.670 4785.5 1463.0
## + test_prep:reading_score 1 1.067 4786.1 1463.1
## + is_first_child:math_score 1 1.040 4786.1 1463.1
## + parent_educ:test_prep 5 65.065 4722.1 1463.1
## + gender:transport_means 1 0.574 4786.6 1463.1
## + gender:test_prep 1 0.401 4786.7 1463.2
## + lunch_type:transport_means 1 0.222 4786.9 1463.2
## + is_first_child:transport_means 1 0.149 4787.0 1463.2
## + lunch_type:test_prep 1 0.116 4787.0 1463.2
## + gender:is_first_child 1 0.098 4787.0 1463.2
## + gender:lunch_type 1 0.004 4787.1 1463.2
## + wkly_study_hours:reading_score 2 11.403 4775.7 1463.8
## + lunch_type:wkly_study_hours 2 10.310 4776.8 1463.9
## + ethnic_group:wkly_study_hours 8 104.720 4682.4 1464.2
## + lunch_type:practice_sport 2 7.829 4779.3 1464.2
## - ethnic_group:math_score 4 91.289 4878.4 1464.3
## + gender:wkly_study_hours 2 6.739 4780.4 1464.4
## - gender:reading_score 1 42.618 4829.8 1464.4
## - ethnic_group:test_prep 4 93.274 4880.4 1464.6
## + practice_sport:transport_means 2 3.861 4783.3 1464.7
## - parent_educ:lunch_type 5 111.284 4898.4 1464.8
## + wkly_study_hours:math_score 2 1.857 4785.3 1465.0
## + is_first_child:wkly_study_hours 2 1.478 4785.7 1465.0
## + gender:parent_marital_status 3 17.130 4770.0 1465.1
## + gender:practice_sport 2 0.601 4786.5 1465.1
## + parent_marital_status:is_first_child 3 16.147 4771.0 1465.2
## + parent_marital_status:math_score 3 10.177 4777.0 1466.0
## + parent_marital_status:transport_means 3 10.032 4777.1 1466.0
## - parent_educ:math_score 5 121.293 4908.4 1466.0
## + ethnic_group:reading_score 4 25.334 4761.8 1466.1
## - parent_educ:transport_means 5 123.261 4910.4 1466.2
## + parent_marital_status:reading_score 3 4.961 4782.2 1466.6
## + gender:parent_educ 5 37.078 4750.1 1466.6
## + ethnic_group:transport_means 4 18.962 4768.2 1466.9
## + ethnic_group:practice_sport 8 82.210 4704.9 1467.0
## + ethnic_group:parent_marital_status 11 126.117 4661.0 1467.5
## + practice_sport:wkly_study_hours 4 6.818 4780.3 1468.4
## - parent_marital_status:wkly_study_hours 6 166.713 4953.9 1469.4
## + parent_marital_status:practice_sport 5 4.570 4782.6 1470.6
## - math_score:reading_score 1 99.386 4886.5 1471.3
## - parent_educ:practice_sport 10 261.961 5049.1 1472.6
## + ethnic_group:parent_educ 20 214.826 4572.3 1474.1
## - parent_educ:is_first_child 5 204.064 4991.2 1475.8
## + parent_educ:wkly_study_hours 10 33.581 4753.6 1477.0
## + parent_educ:parent_marital_status 15 97.720 4689.4 1479.0
##
## Step: AIC=1459.36
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:wkly_study_hours +
## transport_means:math_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 20.596 4809.0 1457.9
## - transport_means:math_score 1 4.894 4793.3 1458.0
## - transport_means:reading_score 1 5.662 4794.1 1458.1
## - test_prep:math_score 1 8.998 4797.4 1458.5
## - test_prep:is_first_child 1 11.598 4800.0 1458.8
## - test_prep:wkly_study_hours 2 28.942 4817.4 1458.9
## - test_prep:parent_marital_status 3 46.457 4834.9 1459.1
## - ethnic_group:lunch_type 4 63.357 4851.8 1459.1
## - lunch_type:is_first_child 1 14.927 4803.4 1459.2
## <none> 4788.4 1459.4
## - test_prep:transport_means 1 16.576 4805.0 1459.4
## - practice_sport:math_score 2 36.317 4824.8 1459.8
## - lunch_type:parent_marital_status 3 54.200 4842.6 1460.0
## - gender:math_score 1 21.879 4810.3 1460.0
## - ethnic_group:is_first_child 4 72.343 4860.8 1460.2
## - practice_sport:is_first_child 2 40.161 4828.6 1460.3
## - test_prep:practice_sport 2 42.186 4830.6 1460.5
## - parent_educ:reading_score 5 92.311 4880.8 1460.6
## - practice_sport:reading_score 2 43.815 4832.3 1460.7
## - gender:ethnic_group 4 78.266 4866.7 1460.9
## + is_first_child:reading_score 1 1.874 4786.6 1461.1
## + lunch_type:math_score 1 1.298 4787.1 1461.2
## + test_prep:reading_score 1 1.230 4787.2 1461.2
## + is_first_child:math_score 1 1.190 4787.3 1461.2
## + gender:transport_means 1 0.700 4787.7 1461.3
## + gender:test_prep 1 0.414 4788.0 1461.3
## + lunch_type:transport_means 1 0.235 4788.2 1461.3
## + parent_educ:test_prep 5 64.646 4723.8 1461.3
## + is_first_child:transport_means 1 0.121 4788.3 1461.3
## + gender:is_first_child 1 0.090 4788.4 1461.3
## + gender:lunch_type 1 0.032 4788.4 1461.4
## + lunch_type:reading_score 1 0.013 4788.4 1461.4
## + lunch_type:test_prep 1 0.007 4788.4 1461.4
## + wkly_study_hours:reading_score 2 11.373 4777.1 1462.0
## + lunch_type:wkly_study_hours 2 11.085 4777.4 1462.0
## + lunch_type:practice_sport 2 7.900 4780.5 1462.4
## + gender:wkly_study_hours 2 6.968 4781.5 1462.5
## - gender:reading_score 1 42.447 4830.9 1462.6
## + ethnic_group:wkly_study_hours 8 102.611 4685.8 1462.6
## - parent_educ:lunch_type 5 110.253 4898.7 1462.8
## - ethnic_group:test_prep 4 94.023 4882.5 1462.8
## + practice_sport:transport_means 2 3.843 4784.6 1462.9
## - ethnic_group:math_score 4 95.917 4884.4 1463.1
## + wkly_study_hours:math_score 2 1.846 4786.6 1463.1
## + is_first_child:wkly_study_hours 2 1.442 4787.0 1463.2
## + gender:parent_marital_status 3 16.933 4771.5 1463.3
## + gender:practice_sport 2 0.552 4787.9 1463.3
## + parent_marital_status:is_first_child 3 15.346 4773.1 1463.5
## - parent_educ:math_score 5 120.935 4909.4 1464.1
## + ethnic_group:reading_score 4 26.501 4761.9 1464.1
## + parent_marital_status:transport_means 3 10.042 4778.4 1464.1
## + parent_marital_status:math_score 3 9.703 4778.7 1464.2
## - parent_educ:transport_means 5 124.461 4912.9 1464.5
## + gender:parent_educ 5 37.925 4750.5 1464.7
## + parent_marital_status:reading_score 3 4.955 4783.5 1464.8
## + ethnic_group:transport_means 4 18.948 4769.5 1465.0
## + ethnic_group:practice_sport 8 80.705 4707.7 1465.3
## + ethnic_group:parent_marital_status 11 125.313 4663.1 1465.7
## + practice_sport:wkly_study_hours 4 6.926 4781.5 1466.5
## - parent_marital_status:wkly_study_hours 6 167.095 4955.5 1467.6
## + parent_marital_status:practice_sport 5 4.577 4783.9 1468.8
## - parent_educ:practice_sport 10 264.481 5052.9 1471.1
## - math_score:reading_score 1 121.656 4910.1 1472.2
## + ethnic_group:parent_educ 20 210.232 4578.2 1472.9
## - parent_educ:is_first_child 5 205.050 4993.5 1474.1
## + parent_educ:wkly_study_hours 10 33.164 4755.3 1475.3
## + parent_educ:parent_marital_status 15 96.429 4692.0 1477.4
##
## Step: AIC=1457.9
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:math_score +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - transport_means:math_score 1 4.513 4813.6 1456.5
## - transport_means:reading_score 1 5.286 4814.3 1456.5
## - test_prep:math_score 1 7.259 4816.3 1456.8
## - ethnic_group:lunch_type 4 59.169 4868.2 1457.1
## - test_prep:is_first_child 1 10.441 4819.5 1457.2
## - test_prep:wkly_study_hours 2 26.860 4835.9 1457.2
## - test_prep:parent_marital_status 3 43.513 4852.6 1457.2
## - lunch_type:is_first_child 1 15.607 4824.6 1457.8
## <none> 4809.0 1457.9
## - test_prep:transport_means 1 17.638 4826.7 1458.1
## - practice_sport:math_score 2 34.722 4843.8 1458.1
## - ethnic_group:is_first_child 4 70.781 4879.8 1458.5
## - practice_sport:is_first_child 2 39.548 4848.6 1458.7
## - gender:math_score 1 23.368 4832.4 1458.8
## - test_prep:practice_sport 2 41.104 4850.1 1458.9
## - lunch_type:parent_marital_status 3 58.290 4867.3 1459.0
## - parent_educ:reading_score 5 92.119 4901.2 1459.1
## - practice_sport:reading_score 2 42.543 4851.6 1459.1
## + transport_means:wkly_study_hours 2 20.596 4788.4 1459.4
## + is_first_child:reading_score 1 2.165 4806.9 1459.6
## - gender:ethnic_group 4 80.253 4889.3 1459.7
## + is_first_child:math_score 1 1.768 4807.3 1459.7
## + lunch_type:math_score 1 1.434 4807.6 1459.7
## + gender:transport_means 1 0.997 4808.0 1459.8
## + test_prep:reading_score 1 0.549 4808.5 1459.8
## + lunch_type:transport_means 1 0.394 4808.6 1459.8
## + is_first_child:transport_means 1 0.096 4808.9 1459.9
## + gender:test_prep 1 0.066 4809.0 1459.9
## + parent_educ:test_prep 5 64.825 4744.2 1459.9
## + gender:lunch_type 1 0.048 4809.0 1459.9
## + lunch_type:test_prep 1 0.034 4809.0 1459.9
## + gender:is_first_child 1 0.032 4809.0 1459.9
## + lunch_type:reading_score 1 0.003 4809.0 1459.9
## - parent_educ:lunch_type 5 103.866 4912.9 1460.5
## - ethnic_group:test_prep 4 87.390 4896.4 1460.5
## + lunch_type:wkly_study_hours 2 10.822 4798.2 1460.6
## + wkly_study_hours:reading_score 2 8.415 4800.6 1460.9
## + gender:wkly_study_hours 2 7.867 4801.2 1460.9
## + lunch_type:practice_sport 2 7.191 4801.8 1461.0
## - ethnic_group:math_score 4 92.414 4901.5 1461.1
## + ethnic_group:wkly_study_hours 8 101.873 4707.2 1461.3
## - gender:reading_score 1 45.048 4854.1 1461.4
## + practice_sport:transport_means 2 3.892 4805.1 1461.4
## + parent_marital_status:is_first_child 3 19.325 4789.7 1461.5
## + is_first_child:wkly_study_hours 2 1.280 4807.8 1461.7
## + wkly_study_hours:math_score 2 0.764 4808.3 1461.8
## + gender:practice_sport 2 0.739 4808.3 1461.8
## + gender:parent_marital_status 3 15.791 4793.3 1462.0
## - parent_educ:transport_means 5 119.806 4928.8 1462.4
## + parent_marital_status:transport_means 3 10.883 4798.2 1462.6
## - parent_educ:math_score 5 121.483 4930.5 1462.6
## + ethnic_group:reading_score 4 25.786 4783.3 1462.7
## + parent_marital_status:math_score 3 8.962 4800.1 1462.8
## + gender:parent_educ 5 36.787 4772.3 1463.4
## + parent_marital_status:reading_score 3 3.796 4805.2 1463.4
## + ethnic_group:practice_sport 8 83.335 4725.7 1463.6
## + ethnic_group:transport_means 4 18.804 4790.2 1463.6
## + ethnic_group:parent_marital_status 11 123.410 4685.6 1464.6
## + practice_sport:wkly_study_hours 4 6.220 4802.8 1465.1
## - parent_marital_status:wkly_study_hours 6 166.201 4975.2 1465.9
## + parent_marital_status:practice_sport 5 6.264 4802.8 1467.1
## - parent_educ:practice_sport 10 247.478 5056.5 1467.5
## - math_score:reading_score 1 121.323 4930.4 1470.6
## + ethnic_group:parent_educ 20 206.123 4602.9 1472.0
## - parent_educ:is_first_child 5 206.011 5015.1 1472.7
## + parent_educ:wkly_study_hours 10 34.346 4774.7 1473.7
## + parent_educ:parent_marital_status 15 98.255 4710.8 1475.7
##
## Step: AIC=1456.45
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:math_score 1 7.591 4821.1 1455.4
## - test_prep:parent_marital_status 3 41.589 4855.1 1455.5
## - ethnic_group:lunch_type 4 58.580 4872.1 1455.6
## - test_prep:wkly_study_hours 2 26.854 4840.4 1455.7
## - test_prep:is_first_child 1 10.520 4824.1 1455.7
## <none> 4813.6 1456.5
## - practice_sport:math_score 2 33.160 4846.7 1456.5
## - lunch_type:is_first_child 1 16.898 4830.5 1456.5
## - test_prep:transport_means 1 17.674 4831.2 1456.6
## - ethnic_group:is_first_child 4 69.775 4883.3 1456.9
## - lunch_type:parent_marital_status 3 56.063 4869.6 1457.3
## - practice_sport:is_first_child 2 39.867 4853.4 1457.3
## - parent_educ:reading_score 5 89.613 4903.2 1457.3
## - test_prep:practice_sport 2 40.154 4853.7 1457.3
## - practice_sport:reading_score 2 40.399 4854.0 1457.4
## - gender:math_score 1 24.567 4838.1 1457.5
## + gender:transport_means 1 4.693 4808.9 1457.9
## + transport_means:math_score 1 4.513 4809.0 1457.9
## + transport_means:wkly_study_hours 2 20.215 4793.3 1458.0
## - gender:ethnic_group 4 79.478 4893.0 1458.1
## + is_first_child:reading_score 1 1.990 4811.6 1458.2
## + is_first_child:math_score 1 1.839 4811.7 1458.2
## + parent_educ:test_prep 5 66.384 4747.2 1458.3
## + lunch_type:math_score 1 1.192 4812.4 1458.3
## + test_prep:reading_score 1 0.321 4813.2 1458.4
## + is_first_child:transport_means 1 0.181 4813.4 1458.4
## + gender:lunch_type 1 0.104 4813.5 1458.4
## + lunch_type:test_prep 1 0.024 4813.5 1458.5
## + gender:test_prep 1 0.020 4813.5 1458.5
## + gender:is_first_child 1 0.009 4813.5 1458.5
## + lunch_type:transport_means 1 0.008 4813.5 1458.5
## + lunch_type:reading_score 1 0.001 4813.6 1458.5
## - ethnic_group:test_prep 4 84.830 4898.4 1458.8
## + lunch_type:wkly_study_hours 2 11.466 4802.1 1459.0
## - parent_educ:lunch_type 5 107.528 4921.1 1459.5
## + gender:wkly_study_hours 2 7.663 4805.9 1459.5
## + lunch_type:practice_sport 2 7.528 4806.0 1459.5
## + wkly_study_hours:reading_score 2 7.137 4806.4 1459.6
## - ethnic_group:math_score 4 92.922 4906.5 1459.7
## + practice_sport:transport_means 2 3.907 4809.6 1460.0
## + ethnic_group:wkly_study_hours 8 99.355 4714.2 1460.1
## + parent_marital_status:is_first_child 3 18.231 4795.3 1460.2
## - gender:reading_score 1 47.285 4860.8 1460.2
## + is_first_child:wkly_study_hours 2 1.342 4812.2 1460.3
## + gender:practice_sport 2 0.748 4812.8 1460.4
## + wkly_study_hours:math_score 2 0.521 4813.0 1460.4
## - transport_means:reading_score 1 49.075 4862.6 1460.4
## + gender:parent_marital_status 3 15.883 4797.7 1460.5
## - parent_educ:transport_means 5 119.457 4933.0 1460.9
## - parent_educ:math_score 5 120.532 4934.1 1461.0
## + parent_marital_status:transport_means 3 10.541 4803.0 1461.2
## + ethnic_group:reading_score 4 26.349 4787.2 1461.2
## + parent_marital_status:math_score 3 8.130 4805.4 1461.5
## + parent_marital_status:reading_score 3 3.486 4810.1 1462.0
## + gender:parent_educ 5 35.890 4777.7 1462.0
## + ethnic_group:practice_sport 8 83.259 4730.3 1462.2
## + ethnic_group:transport_means 4 15.849 4797.7 1462.5
## + ethnic_group:parent_marital_status 11 121.875 4691.7 1463.3
## + practice_sport:wkly_study_hours 4 6.472 4807.1 1463.7
## - parent_marital_status:wkly_study_hours 6 166.179 4979.7 1464.5
## + parent_marital_status:practice_sport 5 6.869 4806.7 1465.6
## - parent_educ:practice_sport 10 249.287 5062.8 1466.2
## - math_score:reading_score 1 119.737 4933.3 1469.0
## + ethnic_group:parent_educ 20 206.020 4607.5 1470.6
## - parent_educ:is_first_child 5 208.684 5022.2 1471.5
## + parent_educ:wkly_study_hours 10 34.734 4778.8 1472.2
## + parent_educ:parent_marital_status 15 98.971 4714.6 1474.2
##
## Step: AIC=1455.38
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:parent_marital_status 3 39.544 4860.7 1454.2
## - test_prep:is_first_child 1 9.596 4830.7 1454.5
## - ethnic_group:lunch_type 4 59.415 4880.6 1454.6
## - lunch_type:is_first_child 1 15.274 4836.4 1455.2
## - test_prep:wkly_study_hours 2 31.812 4853.0 1455.3
## <none> 4821.1 1455.4
## - practice_sport:math_score 2 33.078 4854.2 1455.4
## - test_prep:transport_means 1 18.064 4839.2 1455.6
## - ethnic_group:is_first_child 4 70.391 4891.5 1455.9
## - lunch_type:parent_marital_status 3 54.280 4875.4 1456.0
## - practice_sport:is_first_child 2 39.277 4860.4 1456.2
## - test_prep:practice_sport 2 39.461 4860.6 1456.2
## - practice_sport:reading_score 2 40.024 4861.2 1456.3
## + test_prep:math_score 1 7.591 4813.6 1456.5
## - gender:math_score 1 25.157 4846.3 1456.5
## + test_prep:reading_score 1 6.161 4815.0 1456.6
## - parent_educ:reading_score 5 93.907 4915.1 1456.8
## + transport_means:math_score 1 4.846 4816.3 1456.8
## + gender:transport_means 1 4.577 4816.6 1456.8
## - gender:ethnic_group 4 78.061 4899.2 1456.9
## + transport_means:wkly_study_hours 2 18.396 4802.7 1457.1
## + parent_educ:test_prep 5 66.963 4754.2 1457.1
## + lunch_type:math_score 1 1.827 4819.3 1457.2
## + is_first_child:reading_score 1 1.702 4819.4 1457.2
## + is_first_child:math_score 1 1.387 4819.8 1457.2
## + lunch_type:test_prep 1 0.880 4820.3 1457.3
## + is_first_child:transport_means 1 0.343 4820.8 1457.3
## + lunch_type:reading_score 1 0.097 4821.0 1457.4
## + gender:test_prep 1 0.076 4821.1 1457.4
## + gender:is_first_child 1 0.068 4821.1 1457.4
## + gender:lunch_type 1 0.041 4821.1 1457.4
## + lunch_type:transport_means 1 0.025 4821.1 1457.4
## - ethnic_group:test_prep 4 83.143 4904.3 1457.5
## - parent_educ:lunch_type 5 103.907 4925.1 1458.0
## + lunch_type:wkly_study_hours 2 11.569 4809.6 1458.0
## + gender:wkly_study_hours 2 7.817 4813.3 1458.4
## + wkly_study_hours:reading_score 2 7.797 4813.3 1458.4
## + lunch_type:practice_sport 2 7.348 4813.8 1458.5
## - ethnic_group:math_score 4 94.589 4915.7 1458.8
## + ethnic_group:wkly_study_hours 8 100.936 4720.2 1458.9
## + practice_sport:transport_means 2 3.720 4817.4 1458.9
## - gender:reading_score 1 45.583 4866.7 1458.9
## + parent_marital_status:is_first_child 3 19.341 4801.8 1459.0
## + is_first_child:wkly_study_hours 2 1.392 4819.8 1459.2
## + wkly_study_hours:math_score 2 1.001 4820.1 1459.3
## + gender:practice_sport 2 0.815 4820.3 1459.3
## + gender:parent_marital_status 3 16.639 4804.5 1459.3
## - transport_means:reading_score 1 53.175 4874.3 1459.8
## - parent_educ:transport_means 5 120.874 4942.0 1460.0
## + parent_marital_status:transport_means 3 11.021 4810.1 1460.0
## + ethnic_group:reading_score 4 26.488 4794.7 1460.1
## + parent_marital_status:math_score 3 6.474 4814.7 1460.6
## + ethnic_group:practice_sport 8 86.638 4734.5 1460.7
## + parent_marital_status:reading_score 3 2.974 4818.2 1461.0
## - parent_educ:math_score 5 130.004 4951.2 1461.1
## + gender:parent_educ 5 32.655 4788.5 1461.4
## + ethnic_group:transport_means 4 15.145 4806.0 1461.5
## + ethnic_group:parent_marital_status 11 125.067 4696.1 1461.9
## + practice_sport:wkly_study_hours 4 6.358 4814.8 1462.6
## - parent_marital_status:wkly_study_hours 6 164.431 4985.6 1463.2
## + parent_marital_status:practice_sport 5 6.547 4814.6 1464.6
## - parent_educ:practice_sport 10 252.082 5073.2 1465.5
## + ethnic_group:parent_educ 20 207.951 4613.2 1469.4
## + parent_educ:wkly_study_hours 10 36.367 4784.8 1470.9
## - parent_educ:is_first_child 5 213.866 5035.0 1471.0
## - math_score:reading_score 1 158.103 4979.2 1472.4
## + parent_educ:parent_marital_status 15 99.828 4721.3 1473.0
##
## Step: AIC=1454.2
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:practice_sport + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:math_score + practice_sport:reading_score +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 7.211 4867.9 1453.1
## - ethnic_group:lunch_type 4 61.611 4922.3 1453.6
## - lunch_type:is_first_child 1 12.104 4872.8 1453.7
## - practice_sport:math_score 2 31.347 4892.0 1454.0
## - test_prep:transport_means 1 15.675 4876.4 1454.1
## <none> 4860.7 1454.2
## - test_prep:practice_sport 2 34.169 4894.9 1454.3
## - practice_sport:reading_score 2 37.001 4897.7 1454.7
## - test_prep:wkly_study_hours 2 37.276 4898.0 1454.7
## - practice_sport:is_first_child 2 37.593 4898.3 1454.8
## - ethnic_group:is_first_child 4 72.239 4932.9 1454.9
## - ethnic_group:test_prep 4 73.992 4934.7 1455.1
## - lunch_type:parent_marital_status 3 57.330 4918.0 1455.1
## - gender:math_score 1 24.894 4885.6 1455.2
## - gender:ethnic_group 4 75.399 4936.1 1455.3
## + test_prep:parent_marital_status 3 39.544 4821.1 1455.4
## + test_prep:math_score 1 5.546 4855.1 1455.5
## + test_prep:reading_score 1 3.869 4856.8 1455.7
## + gender:transport_means 1 2.972 4857.7 1455.8
## + transport_means:math_score 1 2.806 4857.9 1455.9
## + is_first_child:reading_score 1 1.518 4859.2 1456.0
## + lunch_type:test_prep 1 1.297 4859.4 1456.0
## + is_first_child:math_score 1 0.967 4859.7 1456.1
## + lunch_type:math_score 1 0.829 4859.9 1456.1
## + is_first_child:transport_means 1 0.308 4860.4 1456.2
## + gender:test_prep 1 0.184 4860.5 1456.2
## + lunch_type:transport_means 1 0.055 4860.6 1456.2
## + lunch_type:reading_score 1 0.021 4860.7 1456.2
## + gender:is_first_child 1 0.013 4860.7 1456.2
## + gender:lunch_type 1 0.000 4860.7 1456.2
## + transport_means:wkly_study_hours 2 16.008 4844.7 1456.2
## - parent_educ:lunch_type 5 101.338 4962.0 1456.4
## + parent_educ:test_prep 5 59.877 4800.8 1456.9
## + lunch_type:wkly_study_hours 2 10.695 4850.0 1456.9
## - parent_educ:reading_score 5 108.106 4968.8 1457.2
## + lunch_type:practice_sport 2 7.741 4852.9 1457.3
## + parent_marital_status:is_first_child 3 23.240 4837.4 1457.4
## + gender:wkly_study_hours 2 6.097 4854.6 1457.5
## + wkly_study_hours:reading_score 2 5.406 4855.3 1457.5
## - gender:reading_score 1 44.730 4905.4 1457.6
## + practice_sport:transport_means 2 3.382 4857.3 1457.8
## + is_first_child:wkly_study_hours 2 2.135 4858.6 1457.9
## + gender:parent_marital_status 3 17.352 4843.3 1458.1
## + gender:practice_sport 2 0.329 4860.4 1458.2
## + wkly_study_hours:math_score 2 0.258 4860.4 1458.2
## - transport_means:reading_score 1 49.471 4910.2 1458.2
## - ethnic_group:math_score 4 100.496 4961.2 1458.3
## + ethnic_group:wkly_study_hours 8 93.199 4767.5 1458.8
## - parent_educ:transport_means 5 123.231 4983.9 1459.0
## + parent_marital_status:math_score 3 9.126 4851.6 1459.1
## + parent_marital_status:transport_means 3 6.186 4854.5 1459.5
## + parent_marital_status:reading_score 3 4.568 4856.1 1459.6
## + ethnic_group:reading_score 4 19.362 4841.3 1459.8
## + gender:parent_educ 5 33.520 4827.2 1460.1
## + ethnic_group:transport_means 4 15.993 4844.7 1460.3
## - parent_educ:math_score 5 137.452 4998.1 1460.7
## + ethnic_group:parent_marital_status 11 125.976 4734.7 1460.7
## + ethnic_group:practice_sport 8 76.322 4784.4 1460.9
## + practice_sport:wkly_study_hours 4 6.196 4854.5 1461.5
## + parent_marital_status:practice_sport 5 7.488 4853.2 1463.3
## - parent_marital_status:wkly_study_hours 6 187.407 5048.1 1464.5
## - parent_educ:practice_sport 10 269.908 5130.6 1466.1
## + parent_educ:wkly_study_hours 10 40.115 4820.6 1469.3
## + ethnic_group:parent_educ 20 199.011 4661.7 1469.5
## - parent_educ:is_first_child 5 214.728 5075.4 1469.7
## - math_score:reading_score 1 152.633 5013.3 1470.4
## + parent_educ:parent_marital_status 15 102.767 4757.9 1471.6
##
## Step: AIC=1453.07
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:math_score +
## practice_sport:reading_score + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:math_score 2 29.148 4897.0 1452.6
## - lunch_type:is_first_child 1 13.322 4881.2 1452.7
## - ethnic_group:lunch_type 4 63.722 4931.6 1452.8
## <none> 4867.9 1453.1
## - test_prep:transport_means 1 16.577 4884.5 1453.1
## - test_prep:practice_sport 2 33.778 4901.7 1453.2
## - practice_sport:reading_score 2 35.211 4903.1 1453.3
## - practice_sport:is_first_child 2 36.303 4904.2 1453.5
## - test_prep:wkly_study_hours 2 37.536 4905.4 1453.6
## - gender:ethnic_group 4 72.661 4940.6 1453.8
## - ethnic_group:is_first_child 4 73.319 4941.2 1453.9
## - lunch_type:parent_marital_status 3 56.600 4924.5 1453.9
## - gender:math_score 1 24.967 4892.9 1454.1
## + test_prep:is_first_child 1 7.211 4860.7 1454.2
## - ethnic_group:test_prep 4 76.824 4944.7 1454.3
## + test_prep:math_score 1 4.972 4862.9 1454.5
## + test_prep:parent_marital_status 3 37.159 4830.7 1454.5
## + test_prep:reading_score 1 3.577 4864.3 1454.6
## + gender:transport_means 1 2.940 4865.0 1454.7
## + transport_means:math_score 1 2.877 4865.0 1454.7
## + lunch_type:test_prep 1 1.145 4866.8 1454.9
## + lunch_type:math_score 1 0.712 4867.2 1455.0
## + is_first_child:reading_score 1 0.568 4867.3 1455.0
## + is_first_child:math_score 1 0.281 4867.6 1455.0
## + gender:test_prep 1 0.192 4867.7 1455.0
## + is_first_child:transport_means 1 0.174 4867.7 1455.0
## + gender:is_first_child 1 0.163 4867.7 1455.0
## + lunch_type:reading_score 1 0.040 4867.9 1455.1
## + gender:lunch_type 1 0.006 4867.9 1455.1
## + lunch_type:transport_means 1 0.006 4867.9 1455.1
## + transport_means:wkly_study_hours 2 15.218 4852.7 1455.2
## - parent_educ:lunch_type 5 101.568 4969.5 1455.3
## + lunch_type:wkly_study_hours 2 12.637 4855.3 1455.5
## - parent_educ:reading_score 5 105.068 4973.0 1455.7
## + parent_educ:test_prep 5 59.441 4808.5 1455.8
## + lunch_type:practice_sport 2 8.120 4859.8 1456.1
## + parent_marital_status:is_first_child 3 24.176 4843.7 1456.1
## + gender:wkly_study_hours 2 5.523 4862.4 1456.4
## - gender:reading_score 1 44.231 4912.1 1456.4
## + wkly_study_hours:reading_score 2 4.576 4863.3 1456.5
## + practice_sport:transport_means 2 3.588 4864.3 1456.6
## + is_first_child:wkly_study_hours 2 2.884 4865.0 1456.7
## - ethnic_group:math_score 4 99.032 4966.9 1457.0
## + gender:practice_sport 2 0.272 4867.6 1457.0
## + wkly_study_hours:math_score 2 0.175 4867.7 1457.0
## + gender:parent_marital_status 3 16.474 4851.4 1457.1
## - transport_means:reading_score 1 50.435 4918.3 1457.2
## + ethnic_group:wkly_study_hours 8 92.156 4775.7 1457.8
## + parent_marital_status:math_score 3 10.117 4857.8 1457.8
## - parent_educ:transport_means 5 124.317 4992.2 1458.0
## + parent_marital_status:transport_means 3 5.830 4862.1 1458.4
## + parent_marital_status:reading_score 3 5.458 4862.4 1458.4
## + ethnic_group:reading_score 4 17.941 4850.0 1458.9
## + gender:parent_educ 5 34.109 4833.8 1458.9
## + ethnic_group:transport_means 4 15.277 4852.6 1459.2
## - parent_educ:math_score 5 135.174 5003.1 1459.2
## + ethnic_group:practice_sport 8 75.787 4792.1 1459.8
## + ethnic_group:parent_marital_status 11 121.039 4746.9 1460.2
## + practice_sport:wkly_study_hours 4 6.509 4861.4 1460.3
## + parent_marital_status:practice_sport 5 7.551 4860.3 1462.2
## - parent_marital_status:wkly_study_hours 6 186.214 5054.1 1463.2
## - parent_educ:practice_sport 10 266.999 5134.9 1464.6
## + parent_educ:wkly_study_hours 10 38.849 4829.1 1468.3
## + ethnic_group:parent_educ 20 198.698 4669.2 1468.5
## - parent_educ:is_first_child 5 214.875 5082.8 1468.6
## - math_score:reading_score 1 153.701 5021.6 1469.4
## + parent_educ:parent_marital_status 15 106.785 4761.1 1470.0
##
## Step: AIC=1452.6
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:reading_score +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:reading_score 2 8.869 4905.9 1449.7
## - ethnic_group:lunch_type 4 59.637 4956.7 1451.7
## - lunch_type:is_first_child 1 13.679 4910.7 1452.2
## <none> 4897.0 1452.6
## - test_prep:practice_sport 2 33.717 4930.8 1452.6
## - test_prep:transport_means 1 17.390 4914.4 1452.7
## - gender:ethnic_group 4 68.000 4965.0 1452.7
## - ethnic_group:is_first_child 4 69.316 4966.4 1452.9
## + practice_sport:math_score 2 29.148 4867.9 1453.1
## - gender:math_score 1 20.844 4917.9 1453.1
## - practice_sport:is_first_child 2 38.263 4935.3 1453.2
## - test_prep:wkly_study_hours 2 38.557 4935.6 1453.2
## - parent_educ:lunch_type 5 92.222 4989.3 1453.6
## - lunch_type:parent_marital_status 3 58.739 4955.8 1453.6
## - ethnic_group:test_prep 4 77.160 4974.2 1453.8
## + test_prep:is_first_child 1 5.012 4892.0 1454.0
## + test_prep:math_score 1 4.975 4892.1 1454.0
## + test_prep:reading_score 1 4.122 4892.9 1454.1
## + test_prep:parent_marital_status 3 35.893 4861.2 1454.3
## + gender:transport_means 1 2.097 4895.0 1454.3
## + transport_means:math_score 1 1.771 4895.3 1454.4
## + lunch_type:math_score 1 1.278 4895.8 1454.4
## + lunch_type:test_prep 1 1.222 4895.8 1454.5
## + is_first_child:reading_score 1 0.351 4896.7 1454.5
## + is_first_child:math_score 1 0.191 4896.9 1454.6
## + gender:test_prep 1 0.135 4896.9 1454.6
## + is_first_child:transport_means 1 0.127 4896.9 1454.6
## + gender:is_first_child 1 0.099 4896.9 1454.6
## + lunch_type:reading_score 1 0.065 4897.0 1454.6
## + gender:lunch_type 1 0.043 4897.0 1454.6
## + lunch_type:transport_means 1 0.010 4897.0 1454.6
## + gender:practice_sport 2 15.618 4881.4 1454.7
## + transport_means:wkly_study_hours 2 14.286 4882.8 1454.9
## + parent_educ:test_prep 5 63.077 4834.0 1455.0
## - parent_educ:reading_score 5 104.299 5001.3 1455.0
## - gender:reading_score 1 37.077 4934.1 1455.0
## + lunch_type:wkly_study_hours 2 11.544 4885.5 1455.2
## - ethnic_group:math_score 4 90.416 4987.5 1455.4
## + parent_marital_status:is_first_child 3 24.139 4872.9 1455.7
## + gender:wkly_study_hours 2 5.991 4891.1 1455.9
## + lunch_type:practice_sport 2 5.753 4891.3 1455.9
## + wkly_study_hours:reading_score 2 4.962 4892.1 1456.0
## + practice_sport:transport_means 2 3.920 4893.1 1456.1
## + is_first_child:wkly_study_hours 2 3.762 4893.3 1456.1
## + wkly_study_hours:math_score 2 0.407 4896.6 1456.5
## + gender:parent_marital_status 3 15.789 4881.3 1456.7
## - transport_means:reading_score 1 52.184 4949.2 1456.8
## - parent_educ:transport_means 5 123.530 5020.6 1457.3
## + parent_marital_status:math_score 3 7.827 4889.2 1457.7
## + ethnic_group:wkly_study_hours 8 89.619 4807.4 1457.7
## + parent_marital_status:transport_means 3 5.465 4891.6 1457.9
## + ethnic_group:reading_score 4 21.802 4875.2 1458.0
## - parent_educ:math_score 5 130.420 5027.5 1458.1
## + parent_marital_status:reading_score 3 4.064 4893.0 1458.1
## + gender:parent_educ 5 34.493 4862.6 1458.4
## + ethnic_group:transport_means 4 15.111 4881.9 1458.8
## + practice_sport:wkly_study_hours 4 12.251 4884.8 1459.1
## + ethnic_group:parent_marital_status 11 120.503 4776.5 1459.9
## + ethnic_group:practice_sport 8 63.689 4833.4 1460.9
## - parent_marital_status:wkly_study_hours 6 176.076 5073.1 1461.4
## + parent_marital_status:practice_sport 5 8.508 4888.5 1461.6
## - parent_educ:practice_sport 10 256.786 5153.8 1462.8
## + ethnic_group:parent_educ 20 213.140 4683.9 1466.3
## - parent_educ:is_first_child 5 203.324 5100.4 1466.6
## + parent_educ:wkly_study_hours 10 45.812 4851.2 1467.0
## + parent_educ:parent_marital_status 15 110.433 4786.6 1469.1
## - math_score:reading_score 1 160.689 5057.7 1469.7
##
## Step: AIC=1449.66
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:practice_sport + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 57.590 4963.5 1448.5
## - test_prep:practice_sport 2 29.524 4935.4 1449.2
## - lunch_type:is_first_child 1 14.122 4920.0 1449.4
## - gender:ethnic_group 4 64.897 4970.8 1449.4
## <none> 4905.9 1449.7
## - test_prep:transport_means 1 16.979 4922.9 1449.7
## - gender:math_score 1 20.576 4926.5 1450.1
## - ethnic_group:is_first_child 4 73.185 4979.1 1450.4
## - test_prep:wkly_study_hours 2 39.617 4945.5 1450.4
## - practice_sport:is_first_child 2 39.775 4945.7 1450.4
## - parent_educ:lunch_type 5 91.564 4997.5 1450.6
## - lunch_type:parent_marital_status 3 59.326 4965.2 1450.8
## + test_prep:is_first_child 1 5.557 4900.4 1451.0
## - ethnic_group:test_prep 4 79.123 4985.0 1451.1
## + test_prep:math_score 1 4.469 4901.4 1451.1
## + test_prep:reading_score 1 3.727 4902.2 1451.2
## + gender:practice_sport 2 19.349 4886.6 1451.3
## + test_prep:parent_marital_status 3 35.592 4870.3 1451.4
## + gender:transport_means 1 1.869 4904.0 1451.4
## + lunch_type:test_prep 1 1.383 4904.5 1451.5
## + transport_means:math_score 1 1.352 4904.6 1451.5
## + lunch_type:math_score 1 0.976 4904.9 1451.5
## + is_first_child:reading_score 1 0.445 4905.5 1451.6
## + is_first_child:math_score 1 0.275 4905.6 1451.6
## + lunch_type:reading_score 1 0.152 4905.8 1451.7
## + gender:test_prep 1 0.095 4905.8 1451.7
## + is_first_child:transport_means 1 0.036 4905.9 1451.7
## + gender:lunch_type 1 0.026 4905.9 1451.7
## + gender:is_first_child 1 0.025 4905.9 1451.7
## + lunch_type:transport_means 1 0.008 4905.9 1451.7
## + transport_means:wkly_study_hours 2 15.140 4890.8 1451.8
## + parent_educ:test_prep 5 63.990 4841.9 1451.9
## - gender:reading_score 1 36.459 4942.4 1452.0
## + lunch_type:wkly_study_hours 2 11.010 4894.9 1452.3
## - parent_educ:reading_score 5 106.834 5012.8 1452.4
## + parent_marital_status:is_first_child 3 27.076 4878.8 1452.4
## + practice_sport:reading_score 2 8.869 4897.0 1452.6
## + lunch_type:practice_sport 2 7.197 4898.7 1452.8
## + gender:wkly_study_hours 2 6.437 4899.5 1452.9
## + wkly_study_hours:reading_score 2 5.963 4900.0 1453.0
## - ethnic_group:math_score 4 94.736 5000.7 1453.0
## + is_first_child:wkly_study_hours 2 4.307 4901.6 1453.2
## + practice_sport:transport_means 2 3.350 4902.6 1453.3
## + practice_sport:math_score 2 2.806 4903.1 1453.3
## + wkly_study_hours:math_score 2 0.555 4905.4 1453.6
## + gender:parent_marital_status 3 14.669 4891.2 1453.9
## - transport_means:reading_score 1 52.264 4958.2 1453.9
## - parent_educ:transport_means 5 120.929 5026.8 1454.0
## + parent_marital_status:math_score 3 8.074 4897.8 1454.7
## + ethnic_group:wkly_study_hours 8 89.289 4816.6 1454.8
## + parent_marital_status:transport_means 3 5.066 4900.9 1455.0
## + ethnic_group:reading_score 4 21.252 4884.7 1455.1
## + parent_marital_status:reading_score 3 4.131 4901.8 1455.2
## + gender:parent_educ 5 34.914 4871.0 1455.5
## - parent_educ:math_score 5 133.908 5039.8 1455.5
## + ethnic_group:transport_means 4 16.936 4889.0 1455.6
## + practice_sport:wkly_study_hours 4 10.966 4895.0 1456.3
## + ethnic_group:parent_marital_status 11 115.542 4790.4 1457.6
## + ethnic_group:practice_sport 8 59.421 4846.5 1458.5
## + parent_marital_status:practice_sport 5 9.100 4896.8 1458.6
## - parent_marital_status:wkly_study_hours 6 178.107 5084.0 1458.7
## - parent_educ:practice_sport 10 275.711 5181.6 1461.9
## + ethnic_group:parent_educ 20 211.776 4694.1 1463.6
## - parent_educ:is_first_child 5 209.854 5115.8 1464.4
## + parent_educ:wkly_study_hours 10 42.304 4863.6 1464.5
## + parent_educ:parent_marital_status 15 112.142 4793.8 1466.0
## - math_score:reading_score 1 164.201 5070.1 1467.1
##
## Step: AIC=1448.55
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## test_prep:practice_sport + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 29.535 4993.0 1448.0
## - test_prep:transport_means 1 12.947 4976.5 1448.1
## - test_prep:wkly_study_hours 2 33.345 4996.9 1448.5
## <none> 4963.5 1448.5
## - lunch_type:is_first_child 1 17.949 4981.5 1448.7
## - gender:math_score 1 18.395 4981.9 1448.7
## - gender:ethnic_group 4 71.565 5035.1 1449.0
## - practice_sport:is_first_child 2 38.657 5002.2 1449.1
## - parent_educ:lunch_type 5 91.280 5054.8 1449.3
## - lunch_type:parent_marital_status 3 58.011 5021.5 1449.4
## - ethnic_group:math_score 4 77.101 5040.6 1449.6
## + test_prep:is_first_child 1 7.483 4956.0 1449.7
## + ethnic_group:lunch_type 4 57.590 4905.9 1449.7
## - ethnic_group:is_first_child 4 77.289 5040.8 1449.7
## - parent_educ:reading_score 5 94.830 5058.3 1449.7
## + test_prep:math_score 1 5.019 4958.5 1450.0
## + gender:practice_sport 2 21.112 4942.4 1450.0
## + test_prep:parent_marital_status 3 37.109 4926.4 1450.1
## + test_prep:reading_score 1 3.124 4960.4 1450.2
## + gender:transport_means 1 2.077 4961.4 1450.3
## + lunch_type:test_prep 1 1.475 4962.0 1450.4
## + transport_means:math_score 1 1.278 4962.2 1450.4
## + parent_educ:test_prep 5 67.894 4895.6 1450.4
## - gender:reading_score 1 32.886 4996.4 1450.5
## + lunch_type:reading_score 1 0.352 4963.2 1450.5
## + lunch_type:math_score 1 0.215 4963.3 1450.5
## + is_first_child:transport_means 1 0.173 4963.3 1450.5
## + gender:test_prep 1 0.140 4963.4 1450.5
## + is_first_child:math_score 1 0.088 4963.4 1450.5
## + gender:is_first_child 1 0.066 4963.4 1450.5
## + lunch_type:transport_means 1 0.060 4963.4 1450.5
## + is_first_child:reading_score 1 0.032 4963.5 1450.5
## + gender:lunch_type 1 0.017 4963.5 1450.5
## + lunch_type:wkly_study_hours 2 14.109 4949.4 1450.9
## - ethnic_group:test_prep 4 87.602 5051.1 1450.9
## + transport_means:wkly_study_hours 2 12.024 4951.5 1451.1
## + parent_marital_status:is_first_child 3 28.559 4934.9 1451.2
## - parent_educ:transport_means 5 110.911 5074.4 1451.6
## + practice_sport:reading_score 2 6.822 4956.7 1451.7
## + gender:wkly_study_hours 2 5.633 4957.9 1451.9
## + lunch_type:practice_sport 2 4.928 4958.6 1452.0
## + practice_sport:transport_means 2 3.077 4960.4 1452.2
## + is_first_child:wkly_study_hours 2 2.765 4960.7 1452.2
## + practice_sport:math_score 2 2.680 4960.8 1452.2
## + wkly_study_hours:reading_score 2 2.570 4960.9 1452.2
## - transport_means:reading_score 1 48.284 5011.8 1452.3
## + wkly_study_hours:math_score 2 0.026 4963.5 1452.5
## - parent_educ:math_score 5 121.085 5084.6 1452.8
## + gender:parent_marital_status 3 13.852 4949.7 1452.9
## + ethnic_group:wkly_study_hours 8 93.425 4870.1 1453.3
## + parent_marital_status:transport_means 3 7.674 4955.8 1453.6
## + parent_marital_status:math_score 3 5.929 4957.6 1453.8
## + gender:parent_educ 5 38.586 4924.9 1454.0
## + parent_marital_status:reading_score 3 2.686 4960.8 1454.2
## + practice_sport:wkly_study_hours 4 12.280 4951.2 1455.1
## + ethnic_group:transport_means 4 11.772 4951.7 1455.2
## + ethnic_group:reading_score 4 11.538 4952.0 1455.2
## + parent_marital_status:practice_sport 5 10.208 4953.3 1457.3
## - parent_marital_status:wkly_study_hours 6 181.841 5145.3 1457.8
## + ethnic_group:practice_sport 8 55.921 4907.6 1457.9
## + ethnic_group:parent_marital_status 11 99.162 4864.3 1458.6
## - parent_educ:practice_sport 10 263.191 5226.7 1459.0
## + parent_educ:wkly_study_hours 10 49.114 4914.4 1462.7
## - parent_educ:is_first_child 5 213.726 5177.2 1463.4
## + ethnic_group:parent_educ 20 206.252 4757.3 1463.5
## - math_score:reading_score 1 162.772 5126.3 1465.6
## + parent_educ:parent_marital_status 15 103.300 4860.2 1466.1
##
## Step: AIC=1448.05
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## transport_means:reading_score + math_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 13.693 5006.7 1447.7
## <none> 4993.0 1448.0
## - test_prep:wkly_study_hours 2 34.710 5027.8 1448.1
## - gender:math_score 1 18.873 5011.9 1448.3
## - gender:ethnic_group 4 70.139 5063.2 1448.3
## - lunch_type:is_first_child 1 19.178 5012.2 1448.3
## - practice_sport:is_first_child 2 36.589 5029.6 1448.4
## + test_prep:practice_sport 2 29.535 4963.5 1448.5
## - lunch_type:parent_marital_status 3 55.552 5048.6 1448.6
## - parent_educ:reading_score 5 93.524 5086.6 1449.0
## - ethnic_group:math_score 4 77.680 5070.7 1449.2
## + ethnic_group:lunch_type 4 57.601 4935.4 1449.2
## - ethnic_group:is_first_child 4 78.091 5071.1 1449.2
## + test_prep:is_first_child 1 6.668 4986.4 1449.3
## - parent_educ:lunch_type 5 96.537 5089.6 1449.3
## + test_prep:math_score 1 4.513 4988.5 1449.5
## + gender:practice_sport 2 21.082 4972.0 1449.5
## + test_prep:reading_score 1 3.621 4989.4 1449.6
## + parent_educ:test_prep 5 70.184 4922.9 1449.7
## - ethnic_group:test_prep 4 82.851 5075.9 1449.8
## + gender:transport_means 1 2.223 4990.8 1449.8
## + lunch_type:test_prep 1 1.819 4991.2 1449.8
## + transport_means:math_score 1 1.120 4991.9 1449.9
## - gender:reading_score 1 32.843 5025.9 1449.9
## + lunch_type:reading_score 1 0.433 4992.6 1450.0
## + is_first_child:math_score 1 0.394 4992.6 1450.0
## + lunch_type:math_score 1 0.217 4992.8 1450.0
## + is_first_child:transport_means 1 0.183 4992.9 1450.0
## + gender:test_prep 1 0.112 4992.9 1450.0
## + is_first_child:reading_score 1 0.104 4992.9 1450.0
## + lunch_type:transport_means 1 0.009 4993.0 1450.0
## + gender:lunch_type 1 0.008 4993.0 1450.0
## + gender:is_first_child 1 0.008 4993.0 1450.0
## + test_prep:parent_marital_status 3 33.480 4959.6 1450.1
## + lunch_type:wkly_study_hours 2 12.191 4980.9 1450.6
## + transport_means:wkly_study_hours 2 12.077 4981.0 1450.6
## + parent_marital_status:is_first_child 3 23.996 4969.0 1451.2
## + practice_sport:math_score 2 5.780 4987.3 1451.4
## + gender:wkly_study_hours 2 5.256 4987.8 1451.4
## + lunch_type:practice_sport 2 5.099 4987.9 1451.5
## + practice_sport:transport_means 2 4.319 4988.7 1451.5
## + practice_sport:reading_score 2 3.641 4989.4 1451.6
## + is_first_child:wkly_study_hours 2 3.047 4990.0 1451.7
## - parent_educ:math_score 5 117.660 5110.7 1451.8
## - transport_means:reading_score 1 49.010 5042.1 1451.8
## + wkly_study_hours:reading_score 2 1.884 4991.2 1451.8
## - parent_educ:transport_means 5 118.034 5111.1 1451.8
## + wkly_study_hours:math_score 2 0.113 4992.9 1452.0
## + gender:parent_marital_status 3 10.576 4982.5 1452.8
## + parent_marital_status:transport_means 3 8.311 4984.7 1453.1
## + ethnic_group:wkly_study_hours 8 91.953 4901.1 1453.1
## + gender:parent_educ 5 40.708 4952.3 1453.2
## + parent_marital_status:math_score 3 5.310 4987.7 1453.4
## + parent_marital_status:reading_score 3 2.543 4990.5 1453.8
## + practice_sport:wkly_study_hours 4 16.272 4976.8 1454.1
## + ethnic_group:transport_means 4 13.498 4979.5 1454.5
## + ethnic_group:reading_score 4 8.447 4984.6 1455.0
## - parent_marital_status:wkly_study_hours 6 173.095 5166.1 1456.2
## + parent_marital_status:practice_sport 5 8.998 4984.0 1457.0
## + ethnic_group:practice_sport 8 54.476 4938.6 1457.6
## + ethnic_group:parent_marital_status 11 98.173 4894.9 1458.3
## - parent_educ:practice_sport 10 282.569 5275.6 1460.5
## + parent_educ:wkly_study_hours 10 51.053 4942.0 1462.0
## + ethnic_group:parent_educ 20 212.063 4781.0 1462.4
## - parent_educ:is_first_child 5 222.902 5215.9 1463.8
## - math_score:reading_score 1 159.018 5152.1 1464.5
## + parent_educ:parent_marital_status 15 103.415 4889.6 1465.7
##
## Step: AIC=1447.67
## writing_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + math_score + reading_score +
## gender:ethnic_group + gender:math_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:math_score +
## parent_educ:lunch_type + parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + parent_educ:reading_score +
## lunch_type:parent_marital_status + lunch_type:is_first_child +
## test_prep:wkly_study_hours + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + transport_means:reading_score +
## math_score:reading_score
##
## Df Sum of Sq RSS AIC
## <none> 5006.7 1447.7
## - lunch_type:is_first_child 1 17.101 5023.8 1447.7
## - test_prep:wkly_study_hours 2 35.503 5042.2 1447.8
## - gender:ethnic_group 4 71.201 5077.9 1448.0
## - gender:math_score 1 20.172 5026.9 1448.0
## + test_prep:transport_means 1 13.693 4993.0 1448.0
## + test_prep:practice_sport 2 30.281 4976.5 1448.1
## - lunch_type:parent_marital_status 3 54.991 5061.7 1448.1
## - practice_sport:is_first_child 2 38.826 5045.6 1448.2
## - ethnic_group:math_score 4 75.283 5082.0 1448.5
## - parent_educ:reading_score 5 95.071 5101.8 1448.8
## + test_prep:is_first_child 1 7.284 4999.5 1448.8
## - ethnic_group:is_first_child 4 79.586 5086.3 1449.0
## + test_prep:math_score 1 4.945 5001.8 1449.1
## + test_prep:reading_score 1 4.470 5002.3 1449.1
## + gender:practice_sport 2 20.819 4985.9 1449.2
## + ethnic_group:lunch_type 4 53.577 4953.2 1449.3
## + lunch_type:test_prep 1 1.784 5005.0 1449.5
## + transport_means:math_score 1 1.148 5005.6 1449.5
## + gender:transport_means 1 1.115 5005.6 1449.5
## - gender:reading_score 1 33.121 5039.9 1449.6
## + parent_educ:test_prep 5 68.199 4938.5 1449.6
## + lunch_type:reading_score 1 0.621 5006.1 1449.6
## - parent_educ:lunch_type 5 102.424 5109.2 1449.6
## + is_first_child:math_score 1 0.284 5006.5 1449.6
## + lunch_type:math_score 1 0.139 5006.6 1449.7
## + is_first_child:reading_score 1 0.069 5006.7 1449.7
## + lunch_type:transport_means 1 0.067 5006.7 1449.7
## + is_first_child:transport_means 1 0.042 5006.7 1449.7
## + gender:lunch_type 1 0.023 5006.7 1449.7
## + gender:is_first_child 1 0.010 5006.7 1449.7
## + gender:test_prep 1 0.009 5006.7 1449.7
## + test_prep:parent_marital_status 3 31.004 4975.7 1450.0
## + lunch_type:wkly_study_hours 2 13.040 4993.7 1450.1
## - ethnic_group:test_prep 4 89.967 5096.7 1450.2
## + transport_means:wkly_study_hours 2 12.528 4994.2 1450.2
## - transport_means:reading_score 1 41.160 5047.9 1450.5
## - parent_educ:transport_means 5 111.350 5118.1 1450.6
## + parent_marital_status:is_first_child 3 25.163 4981.6 1450.7
## + gender:wkly_study_hours 2 6.146 5000.6 1450.9
## + practice_sport:math_score 2 5.843 5000.9 1451.0
## + lunch_type:practice_sport 2 5.460 5001.3 1451.0
## + practice_sport:transport_means 2 4.037 5002.7 1451.2
## + wkly_study_hours:reading_score 2 3.307 5003.4 1451.3
## + practice_sport:reading_score 2 3.166 5003.6 1451.3
## + is_first_child:wkly_study_hours 2 2.699 5004.0 1451.3
## - parent_educ:math_score 5 120.038 5126.8 1451.6
## + wkly_study_hours:math_score 2 0.164 5006.6 1451.7
## + gender:parent_marital_status 3 11.505 4995.2 1452.3
## + gender:parent_educ 5 44.891 4961.8 1452.3
## + parent_marital_status:transport_means 3 7.778 4999.0 1452.8
## + parent_marital_status:math_score 3 4.936 5001.8 1453.1
## + ethnic_group:wkly_study_hours 8 88.359 4918.4 1453.2
## + parent_marital_status:reading_score 3 1.952 5004.8 1453.4
## + practice_sport:wkly_study_hours 4 14.210 4992.5 1454.0
## + ethnic_group:transport_means 4 11.725 4995.0 1454.3
## + ethnic_group:reading_score 4 8.036 4998.7 1454.7
## - parent_marital_status:wkly_study_hours 6 173.417 5180.2 1455.8
## + parent_marital_status:practice_sport 5 8.201 4998.5 1456.7
## + ethnic_group:practice_sport 8 54.682 4952.1 1457.2
## + ethnic_group:parent_marital_status 11 101.721 4905.0 1457.6
## - parent_educ:practice_sport 10 274.151 5280.9 1459.1
## + parent_educ:wkly_study_hours 10 53.714 4953.0 1461.3
## + ethnic_group:parent_educ 20 210.965 4795.8 1462.3
## - math_score:reading_score 1 155.833 5162.6 1463.8
## - parent_educ:is_first_child 5 226.710 5233.4 1463.8
## + parent_educ:parent_marital_status 15 103.775 4903.0 1465.3summary(stepwise_model_write2)##
## Call:
## lm(formula = writing_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + math_score +
## reading_score + gender:ethnic_group + gender:math_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:math_score + parent_educ:lunch_type + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:math_score + parent_educ:reading_score + lunch_type:parent_marital_status +
## lunch_type:is_first_child + test_prep:wkly_study_hours +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## transport_means:reading_score + math_score:reading_score,
## data = df_4_mdl_write2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.9657 -2.0030 0.0213 1.8692 7.4929
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 9.6445037 4.5127588
## gendermale -6.5114045 1.7135103
## ethnic_groupgroup B -8.3857922 3.2849149
## ethnic_groupgroup C -6.0166328 3.1934620
## ethnic_groupgroup D -2.5744505 3.2587321
## ethnic_groupgroup E -5.3119146 3.7496070
## parent_educbachelor's degree -2.9973857 3.1823772
## parent_educhigh school -1.7838156 2.7248502
## parent_educmaster's degree 6.1140140 3.6072864
## parent_educsome college -3.1020032 2.5960042
## parent_educsome high school -1.4232574 2.5056988
## lunch_typestandard 0.4477869 1.0482590
## test_prepnone -4.3303001 1.2882595
## parent_marital_statusmarried -1.7237774 0.9647154
## parent_marital_statussingle -1.2636368 1.0556089
## parent_marital_statuswidowed -1.0260639 2.5355813
## practice_sportregularly 2.6275926 1.2818376
## practice_sportsometimes 2.0495873 1.2638189
## is_first_childyes -1.9449244 1.5377155
## transport_meansschool_bus -3.0246990 1.5733964
## wkly_study_hours> 10 -1.5274396 1.3217426
## wkly_study_hours10-May -3.5627989 0.9998964
## math_score 0.4380746 0.0684638
## reading_score 0.6616880 0.0545786
## gendermale:ethnic_groupgroup B -1.9698990 1.1594194
## gendermale:ethnic_groupgroup C -1.9477103 1.1268362
## gendermale:ethnic_groupgroup D -0.7023720 1.1209408
## gendermale:ethnic_groupgroup E -2.3988290 1.2795874
## gendermale:math_score -0.0617195 0.0436166
## gendermale:reading_score 0.0832689 0.0459233
## ethnic_groupgroup B:test_prepnone 1.3387366 1.3136969
## ethnic_groupgroup C:test_prepnone -0.1980783 1.2648345
## ethnic_groupgroup D:test_prepnone -1.2194398 1.2755736
## ethnic_groupgroup E:test_prepnone 0.3828767 1.3501492
## ethnic_groupgroup B:is_first_childyes 2.0753697 1.2206728
## ethnic_groupgroup C:is_first_childyes 3.1156547 1.1453637
## ethnic_groupgroup D:is_first_childyes 2.0611699 1.1686539
## ethnic_groupgroup E:is_first_childyes 2.5880354 1.2645035
## ethnic_groupgroup B:math_score 0.1096732 0.0423353
## ethnic_groupgroup C:math_score 0.0878905 0.0403791
## ethnic_groupgroup D:math_score 0.0702058 0.0413579
## ethnic_groupgroup E:math_score 0.0638520 0.0463740
## parent_educbachelor's degree:lunch_typestandard -0.6844103 1.1895771
## parent_educhigh school:lunch_typestandard 0.9483806 0.9401266
## parent_educmaster's degree:lunch_typestandard -0.4804909 1.4903982
## parent_educsome college:lunch_typestandard 2.3864722 0.9473051
## parent_educsome high school:lunch_typestandard 0.5992191 0.9902033
## parent_educbachelor's degree:practice_sportregularly 2.1457242 1.7035570
## parent_educhigh school:practice_sportregularly 1.8746993 1.4992648
## parent_educmaster's degree:practice_sportregularly -0.5190348 2.0827015
## parent_educsome college:practice_sportregularly 0.4547936 1.5123630
## parent_educsome high school:practice_sportregularly -1.0613776 1.4964049
## parent_educbachelor's degree:practice_sportsometimes 0.6005963 1.6169653
## parent_educhigh school:practice_sportsometimes 1.1756757 1.4278871
## parent_educmaster's degree:practice_sportsometimes -2.4834386 1.7644790
## parent_educsome college:practice_sportsometimes 1.9047387 1.4769477
## parent_educsome high school:practice_sportsometimes -2.9731665 1.4119638
## parent_educbachelor's degree:is_first_childyes 2.6916133 1.0850313
## parent_educhigh school:is_first_childyes 1.9545744 0.9255417
## parent_educmaster's degree:is_first_childyes -2.4678171 1.4325959
## parent_educsome college:is_first_childyes 2.8513272 0.9320346
## parent_educsome high school:is_first_childyes 2.1110432 0.9163858
## parent_educbachelor's degree:transport_meansschool_bus 0.2283265 1.0706439
## parent_educhigh school:transport_meansschool_bus 1.0958791 0.8999995
## parent_educmaster's degree:transport_meansschool_bus -0.9471291 1.3220984
## parent_educsome college:transport_meansschool_bus -1.0455703 0.9065922
## parent_educsome high school:transport_meansschool_bus 1.6285776 0.9162492
## parent_educbachelor's degree:math_score -0.0804471 0.0600067
## parent_educhigh school:math_score -0.0625786 0.0472331
## parent_educmaster's degree:math_score 0.1435242 0.0846319
## parent_educsome college:math_score -0.0546444 0.0495927
## parent_educsome high school:math_score -0.1092178 0.0480917
## parent_educbachelor's degree:reading_score 0.0957272 0.0623827
## parent_educhigh school:reading_score 0.0116011 0.0509301
## parent_educmaster's degree:reading_score -0.1208817 0.0875665
## parent_educsome college:reading_score 0.0440348 0.0507576
## parent_educsome high school:reading_score 0.0923790 0.0507521
## lunch_typestandard:parent_marital_statusmarried -0.0654145 0.8403535
## lunch_typestandard:parent_marital_statussingle -1.6134573 0.9536181
## lunch_typestandard:parent_marital_statuswidowed -1.7849309 2.2385991
## lunch_typestandard:is_first_childyes -0.8390022 0.6439557
## test_prepnone:wkly_study_hours> 10 0.8887096 0.8984417
## test_prepnone:wkly_study_hours10-May 1.3751968 0.7327249
## parent_marital_statusmarried:wkly_study_hours> 10 0.5059311 1.2701017
## parent_marital_statussingle:wkly_study_hours> 10 1.5241711 1.4383179
## parent_marital_statuswidowed:wkly_study_hours> 10 0.4014271 3.6908441
## parent_marital_statusmarried:wkly_study_hours10-May 3.0172746 0.9604939
## parent_marital_statussingle:wkly_study_hours10-May 3.9778930 1.0695335
## parent_marital_statuswidowed:wkly_study_hours10-May 4.4176050 3.1514433
## practice_sportregularly:is_first_childyes -2.1435734 1.0927088
## practice_sportsometimes:is_first_childyes -1.6813218 1.0702264
## transport_meansschool_bus:reading_score 0.0403894 0.0199814
## math_score:reading_score -0.0019615 0.0004987
## t value Pr(>|t|)
## (Intercept) 2.137 0.033072 *
## gendermale -3.800 0.000163 ***
## ethnic_groupgroup B -2.553 0.010983 *
## ethnic_groupgroup C -1.884 0.060142 .
## ethnic_groupgroup D -0.790 0.429895
## ethnic_groupgroup E -1.417 0.157209
## parent_educbachelor's degree -0.942 0.346717
## parent_educhigh school -0.655 0.512998
## parent_educmaster's degree 1.695 0.090720 .
## parent_educsome college -1.195 0.232690
## parent_educsome high school -0.568 0.570286
## lunch_typestandard 0.427 0.669439
## test_prepnone -3.361 0.000835 ***
## parent_marital_statusmarried -1.787 0.074575 .
## parent_marital_statussingle -1.197 0.231850
## parent_marital_statuswidowed -0.405 0.685897
## practice_sportregularly 2.050 0.040902 *
## practice_sportsometimes 1.622 0.105493
## is_first_childyes -1.265 0.206531
## transport_meansschool_bus -1.922 0.055127 .
## wkly_study_hours> 10 -1.156 0.248390
## wkly_study_hours10-May -3.563 0.000402 ***
## math_score 6.399 3.63e-10 ***
## reading_score 12.124 < 2e-16 ***
## gendermale:ethnic_groupgroup B -1.699 0.089938 .
## gendermale:ethnic_groupgroup C -1.728 0.084524 .
## gendermale:ethnic_groupgroup D -0.627 0.531215
## gendermale:ethnic_groupgroup E -1.875 0.061422 .
## gendermale:math_score -1.415 0.157681
## gendermale:reading_score 1.813 0.070402 .
## ethnic_groupgroup B:test_prepnone 1.019 0.308670
## ethnic_groupgroup C:test_prepnone -0.157 0.875620
## ethnic_groupgroup D:test_prepnone -0.956 0.339540
## ethnic_groupgroup E:test_prepnone 0.284 0.776850
## ethnic_groupgroup B:is_first_childyes 1.700 0.089722 .
## ethnic_groupgroup C:is_first_childyes 2.720 0.006752 **
## ethnic_groupgroup D:is_first_childyes 1.764 0.078395 .
## ethnic_groupgroup E:is_first_childyes 2.047 0.041215 *
## ethnic_groupgroup B:math_score 2.591 0.009863 **
## ethnic_groupgroup C:math_score 2.177 0.029978 *
## ethnic_groupgroup D:math_score 1.698 0.090225 .
## ethnic_groupgroup E:math_score 1.377 0.169166
## parent_educbachelor's degree:lunch_typestandard -0.575 0.565322
## parent_educhigh school:lunch_typestandard 1.009 0.313571
## parent_educmaster's degree:lunch_typestandard -0.322 0.747292
## parent_educsome college:lunch_typestandard 2.519 0.012074 *
## parent_educsome high school:lunch_typestandard 0.605 0.545357
## parent_educbachelor's degree:practice_sportregularly 1.260 0.208421
## parent_educhigh school:practice_sportregularly 1.250 0.211737
## parent_educmaster's degree:practice_sportregularly -0.249 0.803300
## parent_educsome college:practice_sportregularly 0.301 0.763756
## parent_educsome high school:practice_sportregularly -0.709 0.478480
## parent_educbachelor's degree:practice_sportsometimes 0.371 0.710472
## parent_educhigh school:practice_sportsometimes 0.823 0.410694
## parent_educmaster's degree:practice_sportsometimes -1.407 0.159915
## parent_educsome college:practice_sportsometimes 1.290 0.197774
## parent_educsome high school:practice_sportsometimes -2.106 0.035732 *
## parent_educbachelor's degree:is_first_childyes 2.481 0.013443 *
## parent_educhigh school:is_first_childyes 2.112 0.035201 *
## parent_educmaster's degree:is_first_childyes -1.723 0.085579 .
## parent_educsome college:is_first_childyes 3.059 0.002339 **
## parent_educsome high school:is_first_childyes 2.304 0.021653 *
## parent_educbachelor's degree:transport_meansschool_bus 0.213 0.831211
## parent_educhigh school:transport_meansschool_bus 1.218 0.223937
## parent_educmaster's degree:transport_meansschool_bus -0.716 0.474091
## parent_educsome college:transport_meansschool_bus -1.153 0.249343
## parent_educsome high school:transport_meansschool_bus 1.777 0.076107 .
## parent_educbachelor's degree:math_score -1.341 0.180651
## parent_educhigh school:math_score -1.325 0.185817
## parent_educmaster's degree:math_score 1.696 0.090538 .
## parent_educsome college:math_score -1.102 0.271054
## parent_educsome high school:math_score -2.271 0.023572 *
## parent_educbachelor's degree:reading_score 1.535 0.125539
## parent_educhigh school:reading_score 0.228 0.819907
## parent_educmaster's degree:reading_score -1.380 0.168067
## parent_educsome college:reading_score 0.868 0.386059
## parent_educsome high school:reading_score 1.820 0.069330 .
## lunch_typestandard:parent_marital_statusmarried -0.078 0.937985
## lunch_typestandard:parent_marital_statussingle -1.692 0.091286 .
## lunch_typestandard:parent_marital_statuswidowed -0.797 0.425633
## lunch_typestandard:is_first_childyes -1.303 0.193216
## test_prepnone:wkly_study_hours> 10 0.989 0.323062
## test_prepnone:wkly_study_hours10-May 1.877 0.061128 .
## parent_marital_statusmarried:wkly_study_hours> 10 0.398 0.690551
## parent_marital_statussingle:wkly_study_hours> 10 1.060 0.289800
## parent_marital_statuswidowed:wkly_study_hours> 10 0.109 0.913434
## parent_marital_statusmarried:wkly_study_hours10-May 3.141 0.001782 **
## parent_marital_statussingle:wkly_study_hours10-May 3.719 0.000223 ***
## parent_marital_statuswidowed:wkly_study_hours10-May 1.402 0.161608
## practice_sportregularly:is_first_childyes -1.962 0.050354 .
## practice_sportsometimes:is_first_childyes -1.571 0.116820
## transport_meansschool_bus:reading_score 2.021 0.043779 *
## math_score:reading_score -3.933 9.58e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.174 on 497 degrees of freedom
## Multiple R-squared: 0.9648, Adjusted R-squared: 0.9582
## F-statistic: 147.9 on 92 and 497 DF, p-value: < 2.2e-16MAth Score
df_4_mdl_math2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,math_score,writing_score,reading_score)
full_fit_math2=lm(math_score ~ .^2,data=df_4_mdl_math2)summary(full_fit_math2)##
## Call:
## lm(formula = math_score ~ .^2, data = df_4_mdl_math2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.8339 -2.5556 0.0729 2.6772 13.5028
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error
## (Intercept) -10.063553 15.902031
## gendermale 19.979949 5.459084
## ethnic_groupgroup B -9.908045 10.348115
## ethnic_groupgroup C -2.674303 9.698450
## ethnic_groupgroup D -9.291267 10.188392
## ethnic_groupgroup E -1.524115 10.431088
## parent_educbachelor's degree 5.105902 9.603385
## parent_educhigh school 11.274516 7.461425
## parent_educmaster's degree 7.611157 12.261135
## parent_educsome college 12.078740 7.028940
## parent_educsome high school 9.863557 7.124145
## lunch_typestandard 0.183473 5.580042
## test_prepnone 3.845622 5.998419
## parent_marital_statusmarried -5.351981 7.427840
## parent_marital_statussingle -5.776894 8.655300
## parent_marital_statuswidowed 29.751199 18.491697
## practice_sportregularly -3.461686 9.557641
## practice_sportsometimes 0.109714 9.474618
## is_first_childyes -5.079237 5.489364
## transport_meansschool_bus 9.835872 5.235990
## wkly_study_hours> 10 -0.198662 7.886884
## wkly_study_hours10-May -4.915573 6.280515
## writing_score 0.684852 0.559961
## reading_score 0.240577 0.527297
## gendermale:ethnic_groupgroup B 0.726299 2.951228
## gendermale:ethnic_groupgroup C 2.276796 2.787315
## gendermale:ethnic_groupgroup D -0.233296 2.850301
## gendermale:ethnic_groupgroup E 2.280813 3.128047
## gendermale:parent_educbachelor's degree -2.133728 2.269909
## gendermale:parent_educhigh school -0.882648 1.878208
## gendermale:parent_educmaster's degree 1.952760 2.985466
## gendermale:parent_educsome college -0.726275 2.039503
## gendermale:parent_educsome high school -0.361364 1.999148
## gendermale:lunch_typestandard -0.523858 1.442766
## gendermale:test_prepnone -0.723812 1.451024
## gendermale:parent_marital_statusmarried -0.307346 1.916842
## gendermale:parent_marital_statussingle 0.060258 2.142298
## gendermale:parent_marital_statuswidowed -2.429801 8.143220
## gendermale:practice_sportregularly -0.219895 2.295823
## gendermale:practice_sportsometimes 0.137348 2.237267
## gendermale:is_first_childyes -0.086440 1.378812
## gendermale:transport_meansschool_bus -0.956230 1.365940
## gendermale:wkly_study_hours> 10 0.398251 1.960905
## gendermale:wkly_study_hours10-May -0.385080 1.534527
## gendermale:writing_score -0.141074 0.162549
## gendermale:reading_score 0.075694 0.159839
## ethnic_groupgroup B:parent_educbachelor's degree 0.266536 6.073313
## ethnic_groupgroup C:parent_educbachelor's degree -0.409047 6.020229
## ethnic_groupgroup D:parent_educbachelor's degree 5.112680 5.922853
## ethnic_groupgroup E:parent_educbachelor's degree 3.128234 6.753621
## ethnic_groupgroup B:parent_educhigh school 4.280505 3.674482
## ethnic_groupgroup C:parent_educhigh school 3.348883 3.501663
## ethnic_groupgroup D:parent_educhigh school 4.483079 3.582679
## ethnic_groupgroup E:parent_educhigh school 4.840534 3.987015
## ethnic_groupgroup B:parent_educmaster's degree -5.305727 8.241169
## ethnic_groupgroup C:parent_educmaster's degree -4.417568 7.468955
## ethnic_groupgroup D:parent_educmaster's degree -3.655068 7.623938
## ethnic_groupgroup E:parent_educmaster's degree -7.258787 7.987115
## ethnic_groupgroup B:parent_educsome college 1.180947 4.107385
## ethnic_groupgroup C:parent_educsome college -2.520179 3.822148
## ethnic_groupgroup D:parent_educsome college 4.656424 4.059229
## ethnic_groupgroup E:parent_educsome college 0.868305 4.119982
## ethnic_groupgroup B:parent_educsome high school 3.931608 3.971208
## ethnic_groupgroup C:parent_educsome high school 5.763745 3.640055
## ethnic_groupgroup D:parent_educsome high school 6.721231 3.619185
## ethnic_groupgroup E:parent_educsome high school 8.083832 3.997528
## ethnic_groupgroup B:lunch_typestandard 0.649125 2.845967
## ethnic_groupgroup C:lunch_typestandard 0.149832 2.781119
## ethnic_groupgroup D:lunch_typestandard 0.013271 2.852599
## ethnic_groupgroup E:lunch_typestandard 1.126956 3.135033
## ethnic_groupgroup B:test_prepnone 1.194401 3.148845
## ethnic_groupgroup C:test_prepnone 2.898886 3.013236
## ethnic_groupgroup D:test_prepnone 3.927748 3.059021
## ethnic_groupgroup E:test_prepnone 2.355490 3.166365
## ethnic_groupgroup B:parent_marital_statusmarried -0.496261 3.994810
## ethnic_groupgroup C:parent_marital_statusmarried 1.607295 3.607491
## ethnic_groupgroup D:parent_marital_statusmarried 0.160941 3.624540
## ethnic_groupgroup E:parent_marital_statusmarried 1.840181 3.909171
## ethnic_groupgroup B:parent_marital_statussingle -1.465260 4.720518
## ethnic_groupgroup C:parent_marital_statussingle -1.662000 4.440701
## ethnic_groupgroup D:parent_marital_statussingle -2.754752 4.374864
## ethnic_groupgroup E:parent_marital_statussingle 0.221434 4.910902
## ethnic_groupgroup B:parent_marital_statuswidowed 53.999583 46.909620
## ethnic_groupgroup C:parent_marital_statuswidowed 43.335261 39.315988
## ethnic_groupgroup D:parent_marital_statuswidowed 24.204499 37.893825
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 2.178723 4.822899
## ethnic_groupgroup C:practice_sportregularly -2.765314 4.824426
## ethnic_groupgroup D:practice_sportregularly 0.522775 5.327167
## ethnic_groupgroup E:practice_sportregularly 1.889530 4.895585
## ethnic_groupgroup B:practice_sportsometimes -1.027920 5.181840
## ethnic_groupgroup C:practice_sportsometimes -4.658836 5.029009
## ethnic_groupgroup D:practice_sportsometimes -2.547327 5.540338
## ethnic_groupgroup E:practice_sportsometimes -2.423983 5.074061
## ethnic_groupgroup B:is_first_childyes 2.253002 2.795124
## ethnic_groupgroup C:is_first_childyes -1.900435 2.623197
## ethnic_groupgroup D:is_first_childyes 0.801293 2.692236
## ethnic_groupgroup E:is_first_childyes 1.905110 2.995054
## ethnic_groupgroup B:transport_meansschool_bus 1.299631 2.764491
## ethnic_groupgroup C:transport_meansschool_bus -0.382605 2.516104
## ethnic_groupgroup D:transport_meansschool_bus 1.299017 2.578520
## ethnic_groupgroup E:transport_meansschool_bus -0.438980 2.964843
## ethnic_groupgroup B:wkly_study_hours> 10 -1.612323 4.522319
## ethnic_groupgroup C:wkly_study_hours> 10 0.750639 4.460950
## ethnic_groupgroup D:wkly_study_hours> 10 -0.030054 4.584488
## ethnic_groupgroup E:wkly_study_hours> 10 -3.704460 4.783248
## ethnic_groupgroup B:wkly_study_hours10-May 0.880976 3.750203
## ethnic_groupgroup C:wkly_study_hours10-May 1.603776 3.678274
## ethnic_groupgroup D:wkly_study_hours10-May 2.294593 3.788306
## ethnic_groupgroup E:wkly_study_hours10-May -0.205759 3.997181
## ethnic_groupgroup B:writing_score 0.345499 0.385190
## ethnic_groupgroup C:writing_score 0.772633 0.385880
## ethnic_groupgroup D:writing_score 0.329808 0.369938
## ethnic_groupgroup E:writing_score 0.391206 0.423163
## ethnic_groupgroup B:reading_score -0.273203 0.350590
## ethnic_groupgroup C:reading_score -0.736787 0.346373
## ethnic_groupgroup D:reading_score -0.300445 0.328527
## ethnic_groupgroup E:reading_score -0.392592 0.379670
## parent_educbachelor's degree:lunch_typestandard 2.806697 2.334257
## parent_educhigh school:lunch_typestandard 0.351138 1.917046
## parent_educmaster's degree:lunch_typestandard 7.747509 3.797623
## parent_educsome college:lunch_typestandard -1.011932 1.954360
## parent_educsome high school:lunch_typestandard 2.357029 2.032294
## parent_educbachelor's degree:test_prepnone -3.744743 2.262348
## parent_educhigh school:test_prepnone -4.623184 2.230928
## parent_educmaster's degree:test_prepnone -1.544119 3.901916
## parent_educsome college:test_prepnone -2.136444 2.034417
## parent_educsome high school:test_prepnone -0.252416 2.014710
## parent_educbachelor's degree:parent_marital_statusmarried -0.242286 3.989639
## parent_educhigh school:parent_marital_statusmarried 0.147874 2.715992
## parent_educmaster's degree:parent_marital_statusmarried -0.990220 3.975562
## parent_educsome college:parent_marital_statusmarried -2.845243 2.585056
## parent_educsome high school:parent_marital_statusmarried -3.677034 2.555259
## parent_educbachelor's degree:parent_marital_statussingle -3.105257 4.433246
## parent_educhigh school:parent_marital_statussingle -2.274837 2.908985
## parent_educmaster's degree:parent_marital_statussingle -2.966605 4.070481
## parent_educsome college:parent_marital_statussingle -4.249023 2.847743
## parent_educsome high school:parent_marital_statussingle -7.265951 2.885139
## parent_educbachelor's degree:parent_marital_statuswidowed -25.157857 38.391984
## parent_educhigh school:parent_marital_statuswidowed -56.697558 42.960058
## parent_educmaster's degree:parent_marital_statuswidowed -18.315841 23.322283
## parent_educsome college:parent_marital_statuswidowed -44.785634 29.087158
## parent_educsome high school:parent_marital_statuswidowed -49.558775 34.314653
## parent_educbachelor's degree:practice_sportregularly -1.878258 4.113427
## parent_educhigh school:practice_sportregularly -3.026737 3.403576
## parent_educmaster's degree:practice_sportregularly -2.889508 4.825030
## parent_educsome college:practice_sportregularly -0.934756 3.322442
## parent_educsome high school:practice_sportregularly -0.508045 3.143744
## parent_educbachelor's degree:practice_sportsometimes -0.928893 3.843274
## parent_educhigh school:practice_sportsometimes -2.820167 3.170622
## parent_educmaster's degree:practice_sportsometimes 1.517356 4.320902
## parent_educsome college:practice_sportsometimes -1.707788 3.263860
## parent_educsome high school:practice_sportsometimes 1.501770 3.009011
## parent_educbachelor's degree:is_first_childyes -4.568113 2.240752
## parent_educhigh school:is_first_childyes 0.296732 1.979188
## parent_educmaster's degree:is_first_childyes -0.359355 3.556613
## parent_educsome college:is_first_childyes -2.848291 1.954179
## parent_educsome high school:is_first_childyes -3.015449 2.009189
## parent_educbachelor's degree:transport_meansschool_bus 3.417597 2.251578
## parent_educhigh school:transport_meansschool_bus -0.892789 1.859944
## parent_educmaster's degree:transport_meansschool_bus 5.137701 2.843312
## parent_educsome college:transport_meansschool_bus 1.077925 1.838100
## parent_educsome high school:transport_meansschool_bus -0.425194 1.983677
## parent_educbachelor's degree:wkly_study_hours> 10 -4.895661 3.340936
## parent_educhigh school:wkly_study_hours> 10 -0.988402 2.793862
## parent_educmaster's degree:wkly_study_hours> 10 13.852329 6.344763
## parent_educsome college:wkly_study_hours> 10 0.440856 2.846617
## parent_educsome high school:wkly_study_hours> 10 -2.255143 2.982901
## parent_educbachelor's degree:wkly_study_hours10-May -0.318695 2.380671
## parent_educhigh school:wkly_study_hours10-May 1.516532 2.213374
## parent_educmaster's degree:wkly_study_hours10-May 5.362770 3.326750
## parent_educsome college:wkly_study_hours10-May 2.359546 2.271351
## parent_educsome high school:wkly_study_hours10-May -0.671573 2.402536
## parent_educbachelor's degree:writing_score -0.575083 0.309893
## parent_educhigh school:writing_score -0.241471 0.236755
## parent_educmaster's degree:writing_score -0.987477 0.401391
## parent_educsome college:writing_score -0.111567 0.232350
## parent_educsome high school:writing_score -0.252211 0.239952
## parent_educbachelor's degree:reading_score 0.532131 0.305768
## parent_educhigh school:reading_score 0.127341 0.223323
## parent_educmaster's degree:reading_score 0.781120 0.379454
## parent_educsome college:reading_score 0.018921 0.226178
## parent_educsome high school:reading_score 0.129713 0.227434
## lunch_typestandard:test_prepnone 0.967232 1.564850
## lunch_typestandard:parent_marital_statusmarried 0.413586 1.899033
## lunch_typestandard:parent_marital_statussingle 1.216538 2.240827
## lunch_typestandard:parent_marital_statuswidowed -40.531993 34.813124
## lunch_typestandard:practice_sportregularly 3.093980 2.411249
## lunch_typestandard:practice_sportsometimes 0.889797 2.273015
## lunch_typestandard:is_first_childyes 3.167617 1.531708
## lunch_typestandard:transport_meansschool_bus 0.906158 1.368022
## lunch_typestandard:wkly_study_hours> 10 -1.037156 2.138762
## lunch_typestandard:wkly_study_hours10-May 0.591177 1.575608
## lunch_typestandard:writing_score 0.034891 0.167930
## lunch_typestandard:reading_score -0.083186 0.160327
## test_prepnone:parent_marital_statusmarried 3.711770 1.981008
## test_prepnone:parent_marital_statussingle 4.203078 2.274322
## test_prepnone:parent_marital_statuswidowed -25.734438 19.037555
## test_prepnone:practice_sportregularly 0.622014 2.608208
## test_prepnone:practice_sportsometimes -0.090258 2.532121
## test_prepnone:is_first_childyes -0.100121 1.452427
## test_prepnone:transport_meansschool_bus -3.781701 1.377571
## test_prepnone:wkly_study_hours> 10 -1.704914 2.181380
## test_prepnone:wkly_study_hours10-May -0.499473 1.707231
## test_prepnone:writing_score -0.002329 0.160709
## test_prepnone:reading_score -0.017549 0.153865
## parent_marital_statusmarried:practice_sportregularly 3.691614 2.969841
## parent_marital_statussingle:practice_sportregularly 8.454559 4.002755
## parent_marital_statuswidowed:practice_sportregularly 35.814726 36.605884
## parent_marital_statusmarried:practice_sportsometimes 3.394713 2.916995
## parent_marital_statussingle:practice_sportsometimes 6.154316 3.923684
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes 2.721610 2.325975
## parent_marital_statussingle:is_first_childyes 2.965264 2.518058
## parent_marital_statuswidowed:is_first_childyes 15.630050 13.811686
## parent_marital_statusmarried:transport_meansschool_bus 0.998178 1.877298
## parent_marital_statussingle:transport_meansschool_bus -1.394931 2.108507
## parent_marital_statuswidowed:transport_meansschool_bus -15.572097 8.889319
## parent_marital_statusmarried:wkly_study_hours> 10 -2.240703 3.119485
## parent_marital_statussingle:wkly_study_hours> 10 -4.190052 3.377709
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May -2.935616 2.048140
## parent_marital_statussingle:wkly_study_hours10-May -2.480476 2.292557
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 0.088260 0.236092
## parent_marital_statussingle:writing_score -0.071441 0.261043
## parent_marital_statuswidowed:writing_score NA NA
## parent_marital_statusmarried:reading_score -0.076255 0.237211
## parent_marital_statussingle:reading_score 0.097786 0.261926
## parent_marital_statuswidowed:reading_score NA NA
## practice_sportregularly:is_first_childyes 3.073565 2.674564
## practice_sportsometimes:is_first_childyes 2.274435 2.611838
## practice_sportregularly:transport_meansschool_bus 0.457526 2.281489
## practice_sportsometimes:transport_meansschool_bus -0.873418 2.183510
## practice_sportregularly:wkly_study_hours> 10 -2.679282 3.113849
## practice_sportsometimes:wkly_study_hours> 10 -2.365542 3.078446
## practice_sportregularly:wkly_study_hours10-May 0.248807 2.505147
## practice_sportsometimes:wkly_study_hours10-May 1.249728 2.457903
## practice_sportregularly:writing_score 0.131987 0.299697
## practice_sportsometimes:writing_score 0.262157 0.288717
## practice_sportregularly:reading_score -0.176254 0.279436
## practice_sportsometimes:reading_score -0.286414 0.260580
## is_first_childyes:transport_meansschool_bus -2.449507 1.350503
## is_first_childyes:wkly_study_hours> 10 0.017162 1.996805
## is_first_childyes:wkly_study_hours10-May -2.853518 1.502404
## is_first_childyes:writing_score -0.053821 0.167561
## is_first_childyes:reading_score 0.095788 0.162449
## transport_meansschool_bus:wkly_study_hours> 10 2.207347 1.944391
## transport_meansschool_bus:wkly_study_hours10-May 1.057296 1.386729
## transport_meansschool_bus:writing_score -0.105436 0.166591
## transport_meansschool_bus:reading_score -0.012356 0.160606
## wkly_study_hours> 10:writing_score -0.330908 0.243684
## wkly_study_hours10-May:writing_score -0.323872 0.179972
## wkly_study_hours> 10:reading_score 0.450819 0.237669
## wkly_study_hours10-May:reading_score 0.413381 0.173792
## writing_score:reading_score 0.001094 0.001427
## t value Pr(>|t|)
## (Intercept) -0.633 0.527259
## gendermale 3.660 0.000292 ***
## ethnic_groupgroup B -0.957 0.339009
## ethnic_groupgroup C -0.276 0.782911
## ethnic_groupgroup D -0.912 0.362443
## ethnic_groupgroup E -0.146 0.883919
## parent_educbachelor's degree 0.532 0.595297
## parent_educhigh school 1.511 0.131707
## parent_educmaster's degree 0.621 0.535177
## parent_educsome college 1.718 0.086629 .
## parent_educsome high school 1.385 0.167106
## lunch_typestandard 0.033 0.973789
## test_prepnone 0.641 0.521886
## parent_marital_statusmarried -0.721 0.471694
## parent_marital_statussingle -0.667 0.504944
## parent_marital_statuswidowed 1.609 0.108567
## practice_sportregularly -0.362 0.717435
## practice_sportsometimes 0.012 0.990768
## is_first_childyes -0.925 0.355473
## transport_meansschool_bus 1.879 0.061167 .
## wkly_study_hours> 10 -0.025 0.979919
## wkly_study_hours10-May -0.783 0.434366
## writing_score 1.223 0.222163
## reading_score 0.456 0.648505
## gendermale:ethnic_groupgroup B 0.246 0.805753
## gendermale:ethnic_groupgroup C 0.817 0.414591
## gendermale:ethnic_groupgroup D -0.082 0.934815
## gendermale:ethnic_groupgroup E 0.729 0.466412
## gendermale:parent_educbachelor's degree -0.940 0.347882
## gendermale:parent_educhigh school -0.470 0.638698
## gendermale:parent_educmaster's degree 0.654 0.513497
## gendermale:parent_educsome college -0.356 0.721983
## gendermale:parent_educsome high school -0.181 0.856665
## gendermale:lunch_typestandard -0.363 0.716761
## gendermale:test_prepnone -0.499 0.618223
## gendermale:parent_marital_statusmarried -0.160 0.872709
## gendermale:parent_marital_statussingle 0.028 0.977577
## gendermale:parent_marital_statuswidowed -0.298 0.765593
## gendermale:practice_sportregularly -0.096 0.923751
## gendermale:practice_sportsometimes 0.061 0.951084
## gendermale:is_first_childyes -0.063 0.950049
## gendermale:transport_meansschool_bus -0.700 0.484373
## gendermale:wkly_study_hours> 10 0.203 0.839182
## gendermale:wkly_study_hours10-May -0.251 0.802009
## gendermale:writing_score -0.868 0.386070
## gendermale:reading_score 0.474 0.636113
## ethnic_groupgroup B:parent_educbachelor's degree 0.044 0.965021
## ethnic_groupgroup C:parent_educbachelor's degree -0.068 0.945869
## ethnic_groupgroup D:parent_educbachelor's degree 0.863 0.388629
## ethnic_groupgroup E:parent_educbachelor's degree 0.463 0.643522
## ethnic_groupgroup B:parent_educhigh school 1.165 0.244865
## ethnic_groupgroup C:parent_educhigh school 0.956 0.339565
## ethnic_groupgroup D:parent_educhigh school 1.251 0.211678
## ethnic_groupgroup E:parent_educhigh school 1.214 0.225562
## ethnic_groupgroup B:parent_educmaster's degree -0.644 0.520134
## ethnic_groupgroup C:parent_educmaster's degree -0.591 0.554607
## ethnic_groupgroup D:parent_educmaster's degree -0.479 0.631948
## ethnic_groupgroup E:parent_educmaster's degree -0.909 0.364093
## ethnic_groupgroup B:parent_educsome college 0.288 0.773891
## ethnic_groupgroup C:parent_educsome college -0.659 0.510110
## ethnic_groupgroup D:parent_educsome college 1.147 0.252138
## ethnic_groupgroup E:parent_educsome college 0.211 0.833205
## ethnic_groupgroup B:parent_educsome high school 0.990 0.322864
## ethnic_groupgroup C:parent_educsome high school 1.583 0.114255
## ethnic_groupgroup D:parent_educsome high school 1.857 0.064160 .
## ethnic_groupgroup E:parent_educsome high school 2.022 0.043938 *
## ethnic_groupgroup B:lunch_typestandard 0.228 0.819717
## ethnic_groupgroup C:lunch_typestandard 0.054 0.957067
## ethnic_groupgroup D:lunch_typestandard 0.005 0.996291
## ethnic_groupgroup E:lunch_typestandard 0.359 0.719465
## ethnic_groupgroup B:test_prepnone 0.379 0.704691
## ethnic_groupgroup C:test_prepnone 0.962 0.336708
## ethnic_groupgroup D:test_prepnone 1.284 0.200020
## ethnic_groupgroup E:test_prepnone 0.744 0.457445
## ethnic_groupgroup B:parent_marital_statusmarried -0.124 0.901209
## ethnic_groupgroup C:parent_marital_statusmarried 0.446 0.656210
## ethnic_groupgroup D:parent_marital_statusmarried 0.044 0.964609
## ethnic_groupgroup E:parent_marital_statusmarried 0.471 0.638132
## ethnic_groupgroup B:parent_marital_statussingle -0.310 0.756445
## ethnic_groupgroup C:parent_marital_statussingle -0.374 0.708440
## ethnic_groupgroup D:parent_marital_statussingle -0.630 0.529329
## ethnic_groupgroup E:parent_marital_statussingle 0.045 0.964062
## ethnic_groupgroup B:parent_marital_statuswidowed 1.151 0.250483
## ethnic_groupgroup C:parent_marital_statuswidowed 1.102 0.271141
## ethnic_groupgroup D:parent_marital_statuswidowed 0.639 0.523419
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly 0.452 0.651740
## ethnic_groupgroup C:practice_sportregularly -0.573 0.566895
## ethnic_groupgroup D:practice_sportregularly 0.098 0.921884
## ethnic_groupgroup E:practice_sportregularly 0.386 0.699763
## ethnic_groupgroup B:practice_sportsometimes -0.198 0.842874
## ethnic_groupgroup C:practice_sportsometimes -0.926 0.354899
## ethnic_groupgroup D:practice_sportsometimes -0.460 0.645969
## ethnic_groupgroup E:practice_sportsometimes -0.478 0.633156
## ethnic_groupgroup B:is_first_childyes 0.806 0.420779
## ethnic_groupgroup C:is_first_childyes -0.724 0.469274
## ethnic_groupgroup D:is_first_childyes 0.298 0.766166
## ethnic_groupgroup E:is_first_childyes 0.636 0.525149
## ethnic_groupgroup B:transport_meansschool_bus 0.470 0.638574
## ethnic_groupgroup C:transport_meansschool_bus -0.152 0.879228
## ethnic_groupgroup D:transport_meansschool_bus 0.504 0.614740
## ethnic_groupgroup E:transport_meansschool_bus -0.148 0.882382
## ethnic_groupgroup B:wkly_study_hours> 10 -0.357 0.721668
## ethnic_groupgroup C:wkly_study_hours> 10 0.168 0.866472
## ethnic_groupgroup D:wkly_study_hours> 10 -0.007 0.994773
## ethnic_groupgroup E:wkly_study_hours> 10 -0.774 0.439194
## ethnic_groupgroup B:wkly_study_hours10-May 0.235 0.814417
## ethnic_groupgroup C:wkly_study_hours10-May 0.436 0.663104
## ethnic_groupgroup D:wkly_study_hours10-May 0.606 0.545115
## ethnic_groupgroup E:wkly_study_hours10-May -0.051 0.958976
## ethnic_groupgroup B:writing_score 0.897 0.370377
## ethnic_groupgroup C:writing_score 2.002 0.046050 *
## ethnic_groupgroup D:writing_score 0.892 0.373280
## ethnic_groupgroup E:writing_score 0.924 0.355891
## ethnic_groupgroup B:reading_score -0.779 0.436365
## ethnic_groupgroup C:reading_score -2.127 0.034127 *
## ethnic_groupgroup D:reading_score -0.915 0.361091
## ethnic_groupgroup E:reading_score -1.034 0.301855
## parent_educbachelor's degree:lunch_typestandard 1.202 0.230048
## parent_educhigh school:lunch_typestandard 0.183 0.854777
## parent_educmaster's degree:lunch_typestandard 2.040 0.042113 *
## parent_educsome college:lunch_typestandard -0.518 0.604947
## parent_educsome high school:lunch_typestandard 1.160 0.246949
## parent_educbachelor's degree:test_prepnone -1.655 0.098797 .
## parent_educhigh school:test_prepnone -2.072 0.038989 *
## parent_educmaster's degree:test_prepnone -0.396 0.692550
## parent_educsome college:test_prepnone -1.050 0.294395
## parent_educsome high school:test_prepnone -0.125 0.900371
## parent_educbachelor's degree:parent_marital_statusmarried -0.061 0.951611
## parent_educhigh school:parent_marital_statusmarried 0.054 0.956612
## parent_educmaster's degree:parent_marital_statusmarried -0.249 0.803452
## parent_educsome college:parent_marital_statusmarried -1.101 0.271827
## parent_educsome high school:parent_marital_statusmarried -1.439 0.151069
## parent_educbachelor's degree:parent_marital_statussingle -0.700 0.484127
## parent_educhigh school:parent_marital_statussingle -0.782 0.434757
## parent_educmaster's degree:parent_marital_statussingle -0.729 0.466620
## parent_educsome college:parent_marital_statussingle -1.492 0.136609
## parent_educsome high school:parent_marital_statussingle -2.518 0.012247 *
## parent_educbachelor's degree:parent_marital_statuswidowed -0.655 0.512725
## parent_educhigh school:parent_marital_statuswidowed -1.320 0.187798
## parent_educmaster's degree:parent_marital_statuswidowed -0.785 0.432803
## parent_educsome college:parent_marital_statuswidowed -1.540 0.124562
## parent_educsome high school:parent_marital_statuswidowed -1.444 0.149591
## parent_educbachelor's degree:practice_sportregularly -0.457 0.648238
## parent_educhigh school:practice_sportregularly -0.889 0.374481
## parent_educmaster's degree:practice_sportregularly -0.599 0.549666
## parent_educsome college:practice_sportregularly -0.281 0.778616
## parent_educsome high school:practice_sportregularly -0.162 0.871713
## parent_educbachelor's degree:practice_sportsometimes -0.242 0.809164
## parent_educhigh school:practice_sportsometimes -0.889 0.374381
## parent_educmaster's degree:practice_sportsometimes 0.351 0.725681
## parent_educsome college:practice_sportsometimes -0.523 0.601147
## parent_educsome high school:practice_sportsometimes 0.499 0.618038
## parent_educbachelor's degree:is_first_childyes -2.039 0.042258 *
## parent_educhigh school:is_first_childyes 0.150 0.880912
## parent_educmaster's degree:is_first_childyes -0.101 0.919579
## parent_educsome college:is_first_childyes -1.458 0.145891
## parent_educsome high school:is_first_childyes -1.501 0.134328
## parent_educbachelor's degree:transport_meansschool_bus 1.518 0.129977
## parent_educhigh school:transport_meansschool_bus -0.480 0.631530
## parent_educmaster's degree:transport_meansschool_bus 1.807 0.071655 .
## parent_educsome college:transport_meansschool_bus 0.586 0.557973
## parent_educsome high school:transport_meansschool_bus -0.214 0.830406
## parent_educbachelor's degree:wkly_study_hours> 10 -1.465 0.143748
## parent_educhigh school:wkly_study_hours> 10 -0.354 0.723726
## parent_educmaster's degree:wkly_study_hours> 10 2.183 0.029699 *
## parent_educsome college:wkly_study_hours> 10 0.155 0.877016
## parent_educsome high school:wkly_study_hours> 10 -0.756 0.450159
## parent_educbachelor's degree:wkly_study_hours10-May -0.134 0.893586
## parent_educhigh school:wkly_study_hours10-May 0.685 0.493705
## parent_educmaster's degree:wkly_study_hours10-May 1.612 0.107887
## parent_educsome college:wkly_study_hours10-May 1.039 0.299622
## parent_educsome high school:wkly_study_hours10-May -0.280 0.780011
## parent_educbachelor's degree:writing_score -1.856 0.064355 .
## parent_educhigh school:writing_score -1.020 0.308492
## parent_educmaster's degree:writing_score -2.460 0.014385 *
## parent_educsome college:writing_score -0.480 0.631416
## parent_educsome high school:writing_score -1.051 0.293963
## parent_educbachelor's degree:reading_score 1.740 0.082710 .
## parent_educhigh school:reading_score 0.570 0.568913
## parent_educmaster's degree:reading_score 2.059 0.040300 *
## parent_educsome college:reading_score 0.084 0.933380
## parent_educsome high school:reading_score 0.570 0.568830
## lunch_typestandard:test_prepnone 0.618 0.536924
## lunch_typestandard:parent_marital_statusmarried 0.218 0.827725
## lunch_typestandard:parent_marital_statussingle 0.543 0.587557
## lunch_typestandard:parent_marital_statuswidowed -1.164 0.245130
## lunch_typestandard:practice_sportregularly 1.283 0.200316
## lunch_typestandard:practice_sportsometimes 0.391 0.695702
## lunch_typestandard:is_first_childyes 2.068 0.039393 *
## lunch_typestandard:transport_meansschool_bus 0.662 0.508173
## lunch_typestandard:wkly_study_hours> 10 -0.485 0.628036
## lunch_typestandard:wkly_study_hours10-May 0.375 0.707742
## lunch_typestandard:writing_score 0.208 0.835531
## lunch_typestandard:reading_score -0.519 0.604202
## test_prepnone:parent_marital_statusmarried 1.874 0.061832 .
## test_prepnone:parent_marital_statussingle 1.848 0.065462 .
## test_prepnone:parent_marital_statuswidowed -1.352 0.177347
## test_prepnone:practice_sportregularly 0.238 0.811650
## test_prepnone:practice_sportsometimes -0.036 0.971586
## test_prepnone:is_first_childyes -0.069 0.945083
## test_prepnone:transport_meansschool_bus -2.745 0.006369 **
## test_prepnone:wkly_study_hours> 10 -0.782 0.435008
## test_prepnone:wkly_study_hours10-May -0.293 0.770034
## test_prepnone:writing_score -0.014 0.988446
## test_prepnone:reading_score -0.114 0.909263
## parent_marital_statusmarried:practice_sportregularly 1.243 0.214712
## parent_marital_statussingle:practice_sportregularly 2.112 0.035399 *
## parent_marital_statuswidowed:practice_sportregularly 0.978 0.328579
## parent_marital_statusmarried:practice_sportsometimes 1.164 0.245333
## parent_marital_statussingle:practice_sportsometimes 1.569 0.117694
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes 1.170 0.242783
## parent_marital_statussingle:is_first_childyes 1.178 0.239780
## parent_marital_statuswidowed:is_first_childyes 1.132 0.258577
## parent_marital_statusmarried:transport_meansschool_bus 0.532 0.595274
## parent_marital_statussingle:transport_meansschool_bus -0.662 0.508693
## parent_marital_statuswidowed:transport_meansschool_bus -1.752 0.080714 .
## parent_marital_statusmarried:wkly_study_hours> 10 -0.718 0.473070
## parent_marital_statussingle:wkly_study_hours> 10 -1.241 0.215645
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May -1.433 0.152689
## parent_marital_statussingle:wkly_study_hours10-May -1.082 0.280033
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 0.374 0.708758
## parent_marital_statussingle:writing_score -0.274 0.784501
## parent_marital_statuswidowed:writing_score NA NA
## parent_marital_statusmarried:reading_score -0.321 0.748055
## parent_marital_statussingle:reading_score 0.373 0.709131
## parent_marital_statuswidowed:reading_score NA NA
## practice_sportregularly:is_first_childyes 1.149 0.251288
## practice_sportsometimes:is_first_childyes 0.871 0.384468
## practice_sportregularly:transport_meansschool_bus 0.201 0.841180
## practice_sportsometimes:transport_meansschool_bus -0.400 0.689403
## practice_sportregularly:wkly_study_hours> 10 -0.860 0.390152
## practice_sportsometimes:wkly_study_hours> 10 -0.768 0.442771
## practice_sportregularly:wkly_study_hours10-May 0.099 0.920944
## practice_sportsometimes:wkly_study_hours10-May 0.508 0.611465
## practice_sportregularly:writing_score 0.440 0.659926
## practice_sportsometimes:writing_score 0.908 0.364518
## practice_sportregularly:reading_score -0.631 0.528629
## practice_sportsometimes:reading_score -1.099 0.272484
## is_first_childyes:transport_meansschool_bus -1.814 0.070594 .
## is_first_childyes:wkly_study_hours> 10 0.009 0.993148
## is_first_childyes:wkly_study_hours10-May -1.899 0.058371 .
## is_first_childyes:writing_score -0.321 0.748256
## is_first_childyes:reading_score 0.590 0.555819
## transport_meansschool_bus:wkly_study_hours> 10 1.135 0.257075
## transport_meansschool_bus:wkly_study_hours10-May 0.762 0.446327
## transport_meansschool_bus:writing_score -0.633 0.527221
## transport_meansschool_bus:reading_score -0.077 0.938720
## wkly_study_hours> 10:writing_score -1.358 0.175384
## wkly_study_hours10-May:writing_score -1.800 0.072815 .
## wkly_study_hours> 10:reading_score 1.897 0.058696 .
## wkly_study_hours10-May:reading_score 2.379 0.017930 *
## writing_score:reading_score 0.767 0.443789
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.476 on 340 degrees of freedom
## Multiple R-squared: 0.9334, Adjusted R-squared: 0.8846
## F-statistic: 19.13 on 249 and 340 DF, p-value: < 2.2e-16stepwise_model_math2 <- step(full_fit_math2, direction = "both", trace = 1)## Start: AIC=2181.24
## math_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score)^2
##
## Df Sum of Sq RSS AIC
## - parent_educ:practice_sport 10 154.57 10350 2170.1
## - ethnic_group:parent_marital_status 8 94.75 10290 2170.7
## - ethnic_group:wkly_study_hours 8 107.40 10303 2171.4
## - ethnic_group:lunch_type 4 9.02 10204 2173.8
## - gender:parent_educ 5 55.21 10251 2174.4
## - ethnic_group:practice_sport 8 160.52 10356 2174.5
## - ethnic_group:transport_means 4 53.67 10249 2176.3
## - practice_sport:wkly_study_hours 4 56.41 10252 2176.5
## - parent_educ:parent_marital_status 11 302.90 10498 2176.5
## - gender:parent_marital_status 2 1.95 10197 2177.4
## - gender:practice_sport 2 2.03 10197 2177.4
## - ethnic_group:parent_educ 20 645.97 10841 2177.5
## - gender:wkly_study_hours 2 6.99 10202 2177.7
## - test_prep:practice_sport 2 7.42 10203 2177.7
## - lunch_type:parent_marital_status 2 10.68 10206 2177.9
## - ethnic_group:test_prep 4 81.99 10277 2178.0
## - test_prep:wkly_study_hours 2 19.22 10215 2178.4
## - lunch_type:wkly_study_hours 2 22.66 10218 2178.6
## - parent_marital_status:writing_score 2 22.90 10218 2178.6
## - gender:ethnic_group 4 93.55 10289 2178.6
## - parent_marital_status:reading_score 2 28.08 10224 2178.9
## - practice_sport:transport_means 2 31.09 10226 2179.0
## - test_prep:writing_score 1 0.01 10195 2179.2
## - gender:is_first_child 1 0.12 10196 2179.2
## - test_prep:is_first_child 1 0.14 10196 2179.2
## - transport_means:reading_score 1 0.18 10196 2179.3
## - test_prep:reading_score 1 0.39 10196 2179.3
## - practice_sport:writing_score 2 35.61 10231 2179.3
## - lunch_type:writing_score 1 1.29 10197 2179.3
## - parent_educ:wkly_study_hours 10 318.24 10514 2179.4
## - is_first_child:writing_score 1 3.09 10198 2179.4
## - parent_marital_status:wkly_study_hours 4 107.62 10303 2179.4
## - gender:lunch_type 1 3.95 10199 2179.5
## - transport_means:wkly_study_hours 2 40.69 10236 2179.6
## - gender:reading_score 1 6.72 10202 2179.6
## - practice_sport:is_first_child 2 42.00 10237 2179.7
## - gender:test_prep 1 7.46 10203 2179.7
## - lunch_type:reading_score 1 8.07 10204 2179.7
## - practice_sport:reading_score 2 43.56 10239 2179.8
## - is_first_child:reading_score 1 10.43 10206 2179.8
## - parent_marital_status:is_first_child 2 45.92 10241 2179.9
## - lunch_type:test_prep 1 11.46 10207 2179.9
## - transport_means:writing_score 1 12.01 10207 2179.9
## - lunch_type:transport_means 1 13.16 10208 2180.0
## - gender:transport_means 1 14.70 10210 2180.1
## - writing_score:reading_score 1 17.63 10213 2180.3
## - gender:writing_score 1 22.59 10218 2180.6
## <none> 10195 2181.2
## - parent_marital_status:transport_means 2 74.61 10270 2181.6
## - lunch_type:practice_sport 2 86.55 10282 2182.2
## - parent_educ:test_prep 5 198.51 10394 2182.6
## - parent_marital_status:practice_sport 4 165.02 10360 2182.7
## - wkly_study_hours:writing_score 2 106.46 10302 2183.4
## - parent_educ:transport_means 5 213.35 10409 2183.5
## - parent_educ:reading_score 5 223.98 10419 2184.1
## - test_prep:parent_marital_status 2 120.05 10315 2184.2
## - parent_educ:lunch_type 5 232.17 10428 2184.5
## - ethnic_group:is_first_child 4 200.96 10396 2184.8
## - parent_educ:is_first_child 5 237.74 10433 2184.8
## - is_first_child:transport_means 1 98.65 10294 2184.9
## - is_first_child:wkly_study_hours 2 143.60 10339 2185.5
## - ethnic_group:writing_score 4 215.09 10410 2185.6
## - lunch_type:is_first_child 1 128.24 10324 2186.6
## - parent_educ:writing_score 5 270.10 10466 2186.7
## - ethnic_group:reading_score 4 239.36 10435 2186.9
## - wkly_study_hours:reading_score 2 191.60 10387 2188.2
## - test_prep:transport_means 1 225.98 10421 2192.2
##
## Step: AIC=2170.12
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_marital_status 8 107.27 10457 2160.2
## - ethnic_group:wkly_study_hours 8 112.50 10462 2160.5
## - ethnic_group:lunch_type 4 12.16 10362 2162.8
## - ethnic_group:practice_sport 8 168.40 10518 2163.6
## - gender:parent_educ 5 77.32 10427 2164.5
## - practice_sport:wkly_study_hours 4 58.99 10409 2165.5
## - ethnic_group:transport_means 4 69.53 10420 2166.1
## - ethnic_group:parent_educ 20 650.72 11001 2166.1
## - gender:practice_sport 2 1.17 10351 2166.2
## - parent_educ:parent_marital_status 11 323.23 10673 2166.3
## - gender:parent_marital_status 2 3.78 10354 2166.3
## - gender:wkly_study_hours 2 10.91 10361 2166.7
## - lunch_type:parent_marital_status 2 11.55 10362 2166.8
## - parent_marital_status:writing_score 2 12.85 10363 2166.8
## - ethnic_group:test_prep 4 83.54 10434 2166.9
## - parent_marital_status:reading_score 2 14.61 10365 2166.9
## - test_prep:wkly_study_hours 2 15.41 10365 2167.0
## - test_prep:practice_sport 2 18.72 10369 2167.2
## - lunch_type:wkly_study_hours 2 22.79 10373 2167.4
## - gender:ethnic_group 4 94.95 10445 2167.5
## - practice_sport:transport_means 2 28.70 10379 2167.8
## - transport_means:reading_score 1 0.23 10350 2168.1
## - test_prep:reading_score 1 0.53 10350 2168.2
## - transport_means:wkly_study_hours 2 36.17 10386 2168.2
## - test_prep:is_first_child 1 1.05 10351 2168.2
## - gender:is_first_child 1 1.45 10351 2168.2
## - lunch_type:writing_score 1 2.00 10352 2168.2
## - test_prep:writing_score 1 2.15 10352 2168.2
## - gender:reading_score 1 2.16 10352 2168.2
## - gender:lunch_type 1 2.53 10352 2168.3
## - is_first_child:writing_score 1 2.92 10353 2168.3
## - parent_educ:wkly_study_hours 10 323.76 10674 2168.3
## - practice_sport:writing_score 2 40.63 10391 2168.4
## - practice_sport:is_first_child 2 41.06 10391 2168.5
## - parent_marital_status:wkly_study_hours 4 114.38 10464 2168.6
## - parent_marital_status:is_first_child 2 44.64 10395 2168.7
## - gender:test_prep 1 9.73 10360 2168.7
## - lunch_type:reading_score 1 10.62 10361 2168.7
## - is_first_child:reading_score 1 10.86 10361 2168.7
## - gender:writing_score 1 14.56 10364 2168.9
## - lunch_type:transport_means 1 18.61 10369 2169.2
## - lunch_type:test_prep 1 19.05 10369 2169.2
## - transport_means:writing_score 1 19.51 10370 2169.2
## - gender:transport_means 1 22.93 10373 2169.4
## - practice_sport:reading_score 2 58.48 10408 2169.4
## - writing_score:reading_score 1 27.67 10378 2169.7
## - parent_marital_status:transport_means 2 68.02 10418 2170.0
## <none> 10350 2170.1
## - parent_educ:test_prep 5 193.22 10543 2171.0
## - parent_educ:transport_means 5 200.04 10550 2171.4
## - parent_marital_status:practice_sport 4 166.92 10517 2171.6
## - lunch_type:practice_sport 2 108.18 10458 2172.3
## - wkly_study_hours:writing_score 2 111.81 10462 2172.5
## - test_prep:parent_marital_status 2 120.91 10471 2173.0
## - is_first_child:transport_means 1 101.56 10452 2173.9
## - ethnic_group:writing_score 4 210.66 10561 2174.0
## - ethnic_group:is_first_child 4 211.44 10561 2174.1
## - is_first_child:wkly_study_hours 2 142.36 10492 2174.2
## - parent_educ:is_first_child 5 258.69 10609 2174.7
## - parent_educ:reading_score 5 259.54 10610 2174.7
## - ethnic_group:reading_score 4 230.59 10580 2175.1
## - parent_educ:lunch_type 5 272.42 10622 2175.4
## - lunch_type:is_first_child 1 151.78 10502 2176.7
## - parent_educ:writing_score 5 296.38 10646 2176.8
## - wkly_study_hours:reading_score 2 198.71 10549 2177.3
## - test_prep:transport_means 1 209.35 10559 2179.9
## + parent_educ:practice_sport 10 154.57 10195 2181.2
##
## Step: AIC=2160.21
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:wkly_study_hours 8 115.77 10573 2150.7
## - parent_educ:parent_marital_status 14 366.34 10824 2152.5
## - ethnic_group:lunch_type 4 17.66 10475 2153.2
## - gender:parent_educ 5 76.11 10533 2154.5
## - ethnic_group:practice_sport 8 191.15 10648 2154.9
## - practice_sport:wkly_study_hours 4 63.45 10521 2155.8
## - gender:practice_sport 2 1.58 10459 2156.3
## - gender:parent_marital_status 2 2.03 10459 2156.3
## - gender:wkly_study_hours 2 9.51 10467 2156.7
## - ethnic_group:transport_means 4 83.66 10541 2156.9
## - ethnic_group:parent_educ 20 673.42 11131 2157.0
## - test_prep:wkly_study_hours 2 17.68 10475 2157.2
## - lunch_type:parent_marital_status 2 19.71 10477 2157.3
## - lunch_type:wkly_study_hours 2 20.46 10478 2157.4
## - practice_sport:transport_means 2 21.51 10479 2157.4
## - ethnic_group:test_prep 4 96.31 10554 2157.6
## - test_prep:practice_sport 2 27.33 10484 2157.8
## - gender:ethnic_group 4 100.33 10558 2157.8
## - transport_means:reading_score 1 0.05 10457 2158.2
## - test_prep:reading_score 1 0.30 10458 2158.2
## - parent_marital_status:is_first_child 2 36.34 10494 2158.2
## - test_prep:writing_score 1 0.95 10458 2158.3
## - parent_marital_status:writing_score 2 36.81 10494 2158.3
## - parent_marital_status:reading_score 2 37.04 10494 2158.3
## - lunch_type:writing_score 1 1.82 10459 2158.3
## - gender:lunch_type 1 2.23 10460 2158.3
## - gender:is_first_child 1 2.25 10460 2158.3
## - transport_means:wkly_study_hours 2 38.11 10495 2158.3
## - is_first_child:writing_score 1 3.64 10461 2158.4
## - gender:reading_score 1 4.07 10461 2158.4
## - test_prep:is_first_child 1 6.46 10464 2158.6
## - gender:test_prep 1 7.87 10465 2158.7
## - practice_sport:is_first_child 2 45.38 10503 2158.8
## - is_first_child:reading_score 1 10.84 10468 2158.8
## - parent_marital_status:transport_means 2 46.49 10504 2158.8
## - lunch_type:reading_score 1 11.00 10468 2158.8
## - parent_educ:wkly_study_hours 10 335.36 10793 2158.8
## - practice_sport:writing_score 2 49.45 10507 2159.0
## - transport_means:writing_score 1 15.99 10473 2159.1
## - gender:transport_means 1 16.03 10473 2159.1
## - gender:writing_score 1 18.53 10476 2159.2
## - lunch_type:transport_means 1 20.76 10478 2159.4
## - lunch_type:test_prep 1 23.90 10481 2159.6
## - writing_score:reading_score 1 26.79 10484 2159.7
## <none> 10457 2160.2
## - practice_sport:reading_score 2 78.43 10536 2160.6
## - parent_educ:test_prep 5 186.74 10644 2160.7
## - lunch_type:practice_sport 2 100.64 10558 2161.9
## - parent_educ:transport_means 5 210.27 10668 2161.9
## - parent_marital_status:practice_sport 4 177.54 10635 2162.1
## - wkly_study_hours:writing_score 2 111.12 10568 2162.4
## - parent_marital_status:wkly_study_hours 5 231.47 10689 2163.1
## - is_first_child:wkly_study_hours 2 127.09 10584 2163.3
## - test_prep:parent_marital_status 2 127.24 10584 2163.3
## - ethnic_group:writing_score 4 213.25 10670 2164.1
## - ethnic_group:reading_score 4 221.34 10679 2164.6
## - parent_educ:reading_score 5 263.70 10721 2164.9
## - is_first_child:transport_means 1 123.82 10581 2165.2
## - parent_educ:is_first_child 5 270.93 10728 2165.3
## - parent_educ:lunch_type 5 274.15 10731 2165.5
## - ethnic_group:is_first_child 4 239.12 10696 2165.6
## - parent_educ:writing_score 5 298.78 10756 2166.8
## - lunch_type:is_first_child 1 156.72 10614 2167.0
## - wkly_study_hours:reading_score 2 203.94 10661 2167.6
## - test_prep:transport_means 1 210.66 10668 2170.0
## + ethnic_group:parent_marital_status 8 107.27 10350 2170.1
## + parent_educ:practice_sport 10 167.09 10290 2170.7
##
## Step: AIC=2150.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:parent_marital_status 14 370.44 10943 2143.0
## - ethnic_group:lunch_type 4 21.84 10595 2143.9
## - gender:parent_educ 5 78.71 10652 2145.1
## - ethnic_group:practice_sport 8 190.18 10763 2145.2
## - practice_sport:wkly_study_hours 4 62.38 10635 2146.2
## - parent_educ:wkly_study_hours 10 287.57 10861 2146.5
## - gender:parent_marital_status 2 2.35 10575 2146.8
## - gender:practice_sport 2 2.97 10576 2146.9
## - ethnic_group:transport_means 4 75.16 10648 2146.9
## - gender:wkly_study_hours 2 10.89 10584 2147.3
## - ethnic_group:parent_educ 20 677.80 11251 2147.4
## - test_prep:practice_sport 2 19.80 10593 2147.8
## - ethnic_group:test_prep 4 99.04 10672 2148.2
## - practice_sport:transport_means 2 27.58 10601 2148.2
## - lunch_type:parent_marital_status 2 28.20 10601 2148.3
## - parent_marital_status:is_first_child 2 28.78 10602 2148.3
## - lunch_type:wkly_study_hours 2 30.20 10603 2148.4
## - test_prep:wkly_study_hours 2 35.62 10609 2148.7
## - test_prep:reading_score 1 0.04 10573 2148.7
## - transport_means:reading_score 1 0.05 10573 2148.7
## - test_prep:writing_score 1 0.28 10573 2148.7
## - lunch_type:writing_score 1 1.12 10574 2148.8
## - is_first_child:writing_score 1 1.91 10575 2148.8
## - gender:lunch_type 1 2.40 10575 2148.8
## - gender:reading_score 1 3.09 10576 2148.9
## - practice_sport:writing_score 2 39.76 10613 2148.9
## - gender:ethnic_group 4 112.46 10685 2148.9
## - is_first_child:reading_score 1 6.13 10579 2149.0
## - gender:is_first_child 1 6.77 10580 2149.1
## - lunch_type:reading_score 1 8.11 10581 2149.2
## - gender:test_prep 1 8.31 10581 2149.2
## - transport_means:wkly_study_hours 2 44.84 10618 2149.2
## - test_prep:is_first_child 1 9.07 10582 2149.2
## - parent_marital_status:reading_score 2 46.76 10620 2149.3
## - parent_marital_status:writing_score 2 47.34 10620 2149.3
## - gender:writing_score 1 16.37 10589 2149.6
## - lunch_type:transport_means 1 16.90 10590 2149.6
## - parent_marital_status:transport_means 2 53.05 10626 2149.7
## - gender:transport_means 1 17.94 10591 2149.7
## - practice_sport:is_first_child 2 55.39 10628 2149.8
## - transport_means:writing_score 1 20.63 10594 2149.8
## - writing_score:reading_score 1 25.11 10598 2150.1
## - lunch_type:test_prep 1 26.64 10600 2150.2
## - practice_sport:reading_score 2 68.07 10641 2150.5
## <none> 10573 2150.7
## - parent_educ:test_prep 5 190.39 10763 2151.2
## - parent_educ:transport_means 5 195.37 10768 2151.5
## - lunch_type:practice_sport 2 104.46 10677 2152.5
## - wkly_study_hours:writing_score 2 105.40 10678 2152.6
## - parent_marital_status:wkly_study_hours 5 214.86 10788 2152.6
## - parent_marital_status:practice_sport 4 189.90 10763 2153.2
## - is_first_child:wkly_study_hours 2 125.83 10699 2153.7
## - parent_educ:reading_score 5 247.50 10820 2154.3
## - ethnic_group:writing_score 4 213.57 10787 2154.5
## - ethnic_group:reading_score 4 222.91 10796 2155.0
## - is_first_child:transport_means 1 114.90 10688 2155.1
## - test_prep:parent_marital_status 2 158.65 10732 2155.5
## - ethnic_group:is_first_child 4 239.71 10813 2155.9
## - parent_educ:lunch_type 5 277.05 10850 2156.0
## - parent_educ:writing_score 5 287.71 10861 2156.5
## - parent_educ:is_first_child 5 304.57 10878 2157.5
## - wkly_study_hours:reading_score 2 201.97 10775 2157.9
## - lunch_type:is_first_child 1 182.27 10755 2158.8
## + ethnic_group:wkly_study_hours 8 115.77 10457 2160.2
## - test_prep:transport_means 1 213.41 10786 2160.5
## + ethnic_group:parent_marital_status 8 110.54 10462 2160.5
## + parent_educ:practice_sport 10 171.31 10402 2161.1
##
## Step: AIC=2143.02
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:practice_sport +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:lunch_type 4 19.69 10963 2136.1
## - gender:parent_educ 5 60.12 11004 2136.2
## - ethnic_group:practice_sport 8 183.97 11127 2136.9
## - practice_sport:wkly_study_hours 4 55.26 10999 2138.0
## - parent_educ:wkly_study_hours 10 286.28 11230 2138.3
## - ethnic_group:transport_means 4 69.53 11013 2138.8
## - parent_marital_status:is_first_child 3 33.22 10977 2138.8
## - parent_marital_status:reading_score 3 38.18 10982 2139.1
## - parent_marital_status:writing_score 3 39.30 10983 2139.1
## - gender:practice_sport 2 3.65 10947 2139.2
## - gender:wkly_study_hours 2 3.66 10947 2139.2
## - gender:parent_marital_status 3 52.07 10996 2139.8
## - lunch_type:parent_marital_status 2 21.75 10965 2140.2
## - gender:ethnic_group 4 96.94 11040 2140.2
## - practice_sport:transport_means 2 28.74 10972 2140.6
## - test_prep:practice_sport 2 31.50 10975 2140.7
## - transport_means:reading_score 1 0.01 10943 2141.0
## - test_prep:writing_score 1 0.01 10943 2141.0
## - lunch_type:writing_score 1 0.06 10944 2141.0
## - test_prep:reading_score 1 0.27 10944 2141.0
## - gender:reading_score 1 0.30 10944 2141.0
## - practice_sport:writing_score 2 39.08 10982 2141.1
## - lunch_type:reading_score 1 2.26 10946 2141.1
## - is_first_child:writing_score 1 3.34 10947 2141.2
## - gender:test_prep 1 4.08 10948 2141.2
## - parent_educ:test_prep 5 153.84 11097 2141.3
## - gender:transport_means 1 4.61 10948 2141.3
## - gender:lunch_type 1 4.68 10948 2141.3
## - practice_sport:is_first_child 2 42.51 10986 2141.3
## - lunch_type:transport_means 1 5.58 10949 2141.3
## - gender:is_first_child 1 5.66 10949 2141.3
## - test_prep:wkly_study_hours 2 45.33 10989 2141.5
## - ethnic_group:test_prep 4 120.21 11064 2141.5
## - test_prep:is_first_child 1 8.97 10952 2141.5
## - is_first_child:reading_score 1 9.60 10953 2141.5
## - gender:writing_score 1 9.68 10953 2141.5
## - lunch_type:wkly_study_hours 2 47.89 10991 2141.6
## - lunch_type:test_prep 1 11.05 10954 2141.6
## - transport_means:writing_score 1 14.54 10958 2141.8
## - parent_marital_status:wkly_study_hours 6 203.84 11147 2141.9
## - transport_means:wkly_study_hours 2 54.04 10998 2141.9
## - ethnic_group:parent_educ 20 748.41 11692 2142.1
## - writing_score:reading_score 1 20.63 10964 2142.1
## - parent_educ:transport_means 5 174.89 11118 2142.4
## - practice_sport:reading_score 2 64.53 11008 2142.5
## - parent_marital_status:transport_means 3 106.69 11050 2142.7
## <none> 10943 2143.0
## - wkly_study_hours:writing_score 2 95.34 11039 2144.1
## - parent_marital_status:practice_sport 5 209.74 11153 2144.2
## - lunch_type:practice_sport 2 105.82 11049 2144.7
## - parent_educ:reading_score 5 227.48 11171 2145.2
## - ethnic_group:writing_score 4 208.08 11152 2146.1
## - is_first_child:wkly_study_hours 2 132.78 11076 2146.1
## - ethnic_group:reading_score 4 217.79 11161 2146.7
## - parent_educ:lunch_type 5 259.62 11203 2146.8
## - parent_educ:writing_score 5 269.83 11213 2147.4
## - test_prep:parent_marital_status 3 198.36 11142 2147.6
## - parent_educ:is_first_child 5 278.62 11222 2147.8
## - is_first_child:transport_means 1 135.60 11079 2148.3
## - ethnic_group:is_first_child 4 254.47 11198 2148.6
## - wkly_study_hours:reading_score 2 184.42 11128 2148.9
## + parent_educ:parent_marital_status 14 370.44 10573 2150.7
## - test_prep:transport_means 1 185.79 11129 2150.9
## + parent_educ:practice_sport 10 195.29 10748 2152.4
## - lunch_type:is_first_child 1 213.24 11157 2152.4
## + ethnic_group:wkly_study_hours 8 119.87 10824 2152.5
## + ethnic_group:parent_marital_status 11 160.05 10783 2156.3
##
## Step: AIC=2136.08
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:test_prep + ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:parent_educ 5 62.87 11026 2129.4
## - ethnic_group:practice_sport 8 184.53 11148 2129.9
## - practice_sport:wkly_study_hours 4 53.51 11017 2130.9
## - parent_educ:wkly_study_hours 10 286.33 11250 2131.3
## - parent_marital_status:is_first_child 3 31.01 10994 2131.8
## - parent_marital_status:reading_score 3 35.51 10999 2132.0
## - ethnic_group:transport_means 4 73.49 11037 2132.0
## - parent_marital_status:writing_score 3 36.21 10999 2132.0
## - gender:practice_sport 2 4.42 10968 2132.3
## - gender:wkly_study_hours 2 4.81 10968 2132.3
## - gender:parent_marital_status 3 52.97 11016 2132.9
## - lunch_type:parent_marital_status 2 19.33 10982 2133.1
## - practice_sport:transport_means 2 23.09 10986 2133.3
## - test_prep:practice_sport 2 30.62 10994 2133.7
## - practice_sport:writing_score 2 36.99 11000 2134.1
## - test_prep:writing_score 1 0.01 10963 2134.1
## - gender:reading_score 1 0.07 10963 2134.1
## - transport_means:reading_score 1 0.16 10963 2134.1
## - test_prep:reading_score 1 0.24 10963 2134.1
## - lunch_type:reading_score 1 0.61 10964 2134.1
## - lunch_type:writing_score 1 0.89 10964 2134.1
## - practice_sport:is_first_child 2 38.45 11002 2134.2
## - ethnic_group:test_prep 4 113.36 11076 2134.2
## - gender:ethnic_group 4 113.89 11077 2134.2
## - is_first_child:writing_score 1 2.37 10966 2134.2
## - gender:test_prep 1 3.11 10966 2134.2
## - gender:transport_means 1 4.34 10968 2134.3
## - parent_educ:test_prep 5 154.24 11117 2134.3
## - gender:is_first_child 1 4.61 10968 2134.3
## - lunch_type:transport_means 1 5.45 10969 2134.4
## - gender:lunch_type 1 6.71 10970 2134.4
## - test_prep:is_first_child 1 6.79 10970 2134.4
## - lunch_type:test_prep 1 7.47 10971 2134.5
## - is_first_child:reading_score 1 8.64 10972 2134.6
## - gender:writing_score 1 8.65 10972 2134.6
## - transport_means:writing_score 1 11.42 10974 2134.7
## - test_prep:wkly_study_hours 2 51.20 11014 2134.8
## - parent_marital_status:wkly_study_hours 6 201.69 11165 2134.8
## - lunch_type:wkly_study_hours 2 52.44 11016 2134.9
## - transport_means:wkly_study_hours 2 55.07 11018 2135.0
## - parent_educ:transport_means 5 168.90 11132 2135.1
## - writing_score:reading_score 1 19.62 10983 2135.1
## - practice_sport:reading_score 2 60.53 11024 2135.3
## - parent_marital_status:transport_means 3 108.97 11072 2135.9
## <none> 10963 2136.1
## - ethnic_group:parent_educ 20 778.61 11742 2136.6
## - wkly_study_hours:writing_score 2 89.42 11052 2136.9
## - lunch_type:practice_sport 2 102.29 11065 2137.6
## - parent_marital_status:practice_sport 5 219.27 11182 2137.8
## - parent_educ:reading_score 5 227.21 11190 2138.2
## - is_first_child:wkly_study_hours 2 131.30 11094 2139.1
## - parent_educ:lunch_type 5 264.42 11228 2140.1
## - ethnic_group:writing_score 4 227.60 11191 2140.2
## - ethnic_group:reading_score 4 228.81 11192 2140.3
## - test_prep:parent_marital_status 3 195.00 11158 2140.5
## - parent_educ:writing_score 5 271.51 11235 2140.5
## - parent_educ:is_first_child 5 274.93 11238 2140.7
## - wkly_study_hours:reading_score 2 177.34 11140 2141.6
## - is_first_child:transport_means 1 149.76 11113 2142.1
## + ethnic_group:lunch_type 4 19.69 10943 2143.0
## - ethnic_group:is_first_child 4 281.19 11244 2143.0
## + parent_educ:parent_marital_status 14 368.29 10595 2143.9
## - test_prep:transport_means 1 185.07 11148 2144.0
## + parent_educ:practice_sport 10 204.69 10758 2145.0
## - lunch_type:is_first_child 1 209.37 11172 2145.2
## + ethnic_group:wkly_study_hours 8 121.96 10841 2145.5
## + ethnic_group:parent_marital_status 11 170.18 10793 2148.8
##
## Step: AIC=2129.45
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:wkly_study_hours + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:practice_sport 8 179.30 11205 2123.0
## - parent_educ:wkly_study_hours 10 257.64 11284 2123.1
## - practice_sport:wkly_study_hours 4 48.74 11075 2124.1
## - parent_marital_status:is_first_child 3 28.03 11054 2124.9
## - parent_marital_status:reading_score 3 33.12 11059 2125.2
## - ethnic_group:transport_means 4 70.69 11097 2125.2
## - parent_marital_status:writing_score 3 33.82 11060 2125.3
## - gender:wkly_study_hours 2 3.40 11029 2125.6
## - gender:practice_sport 2 8.55 11034 2125.9
## - gender:parent_marital_status 3 51.57 11078 2126.2
## - lunch_type:parent_marital_status 2 15.07 11041 2126.3
## - practice_sport:transport_means 2 22.97 11049 2126.7
## - test_prep:practice_sport 2 24.29 11050 2126.8
## - gender:ethnic_group 4 101.48 11128 2126.9
## - ethnic_group:test_prep 4 111.34 11137 2127.4
## - transport_means:reading_score 1 0.00 11026 2127.4
## - gender:reading_score 1 0.00 11026 2127.4
## - test_prep:writing_score 1 0.06 11026 2127.5
## - lunch_type:reading_score 1 0.11 11026 2127.5
## - parent_educ:test_prep 5 150.67 11177 2127.5
## - test_prep:reading_score 1 0.36 11026 2127.5
## - gender:test_prep 1 0.58 11027 2127.5
## - lunch_type:transport_means 1 2.29 11028 2127.6
## - is_first_child:writing_score 1 3.44 11029 2127.6
## - lunch_type:writing_score 1 3.60 11030 2127.7
## - gender:is_first_child 1 3.94 11030 2127.7
## - gender:transport_means 1 5.35 11031 2127.7
## - practice_sport:is_first_child 2 43.27 11069 2127.8
## - gender:writing_score 1 7.05 11033 2127.8
## - lunch_type:test_prep 1 8.42 11034 2127.9
## - lunch_type:wkly_study_hours 2 46.06 11072 2127.9
## - test_prep:is_first_child 1 8.66 11035 2127.9
## - gender:lunch_type 1 8.67 11035 2127.9
## - parent_marital_status:wkly_study_hours 6 199.53 11226 2128.0
## - is_first_child:reading_score 1 12.89 11039 2128.1
## - transport_means:writing_score 1 14.98 11041 2128.3
## - writing_score:reading_score 1 15.45 11042 2128.3
## - practice_sport:writing_score 2 54.11 11080 2128.3
## - test_prep:wkly_study_hours 2 59.03 11085 2128.6
## - transport_means:wkly_study_hours 2 61.70 11088 2128.8
## - parent_educ:transport_means 5 179.76 11206 2129.0
## - parent_marital_status:transport_means 3 109.99 11136 2129.3
## <none> 11026 2129.4
## - practice_sport:reading_score 2 76.33 11102 2129.5
## - wkly_study_hours:writing_score 2 86.04 11112 2130.0
## - ethnic_group:parent_educ 20 785.45 11811 2130.1
## - parent_marital_status:practice_sport 5 213.89 11240 2130.8
## - parent_educ:reading_score 5 222.34 11248 2131.2
## - lunch_type:practice_sport 2 112.70 11139 2131.4
## - parent_educ:lunch_type 5 244.91 11271 2132.4
## - is_first_child:wkly_study_hours 2 141.62 11168 2133.0
## - test_prep:parent_marital_status 3 184.77 11211 2133.3
## - parent_educ:is_first_child 5 266.96 11293 2133.6
## - parent_educ:writing_score 5 267.14 11293 2133.6
## - ethnic_group:writing_score 4 246.35 11272 2134.5
## - ethnic_group:reading_score 4 246.69 11273 2134.5
## - wkly_study_hours:reading_score 2 173.45 11199 2134.7
## - is_first_child:transport_means 1 155.00 11181 2135.7
## + gender:parent_educ 5 62.87 10963 2136.1
## + ethnic_group:lunch_type 4 22.45 11004 2136.2
## - test_prep:transport_means 1 178.33 11204 2136.9
## - ethnic_group:is_first_child 4 296.29 11322 2137.1
## + parent_educ:practice_sport 10 220.71 10805 2137.5
## + parent_educ:parent_marital_status 14 351.50 10674 2138.3
## - lunch_type:is_first_child 1 208.52 11234 2138.5
## + ethnic_group:wkly_study_hours 8 128.37 10898 2138.6
## + ethnic_group:parent_marital_status 11 177.45 10849 2141.9
##
## Step: AIC=2122.97
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:wkly_study_hours +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 230.83 11436 2115.0
## - practice_sport:wkly_study_hours 4 44.47 11250 2117.3
## - parent_marital_status:is_first_child 3 24.44 11230 2118.3
## - ethnic_group:transport_means 4 65.46 11271 2118.4
## - parent_marital_status:reading_score 3 35.90 11241 2118.9
## - parent_marital_status:writing_score 3 37.94 11243 2119.0
## - gender:wkly_study_hours 2 1.40 11207 2119.1
## - gender:practice_sport 2 6.08 11211 2119.3
## - test_prep:practice_sport 2 17.82 11223 2119.9
## - gender:parent_marital_status 3 58.81 11264 2120.1
## - practice_sport:transport_means 2 22.02 11227 2120.1
## - gender:ethnic_group 4 98.81 11304 2120.2
## - practice_sport:is_first_child 2 25.68 11231 2120.3
## - ethnic_group:test_prep 4 104.55 11310 2120.4
## - lunch_type:parent_marital_status 2 28.85 11234 2120.5
## - parent_marital_status:wkly_study_hours 6 182.31 11388 2120.5
## - transport_means:wkly_study_hours 2 34.57 11240 2120.8
## - gender:reading_score 1 0.05 11205 2121.0
## - lunch_type:reading_score 1 0.07 11205 2121.0
## - test_prep:writing_score 1 0.18 11206 2121.0
## - transport_means:reading_score 1 0.28 11206 2121.0
## - lunch_type:transport_means 1 0.98 11206 2121.0
## - test_prep:reading_score 1 1.17 11206 2121.0
## - lunch_type:writing_score 1 1.52 11207 2121.1
## - is_first_child:writing_score 1 1.80 11207 2121.1
## - gender:transport_means 1 1.88 11207 2121.1
## - gender:test_prep 1 2.52 11208 2121.1
## - lunch_type:wkly_study_hours 2 42.37 11248 2121.2
## - test_prep:is_first_child 1 4.71 11210 2121.2
## - gender:is_first_child 1 6.04 11211 2121.3
## - gender:lunch_type 1 8.69 11214 2121.4
## - is_first_child:reading_score 1 9.22 11214 2121.5
## - transport_means:writing_score 1 9.35 11215 2121.5
## - gender:writing_score 1 11.33 11217 2121.6
## - lunch_type:test_prep 1 11.49 11217 2121.6
## - parent_educ:test_prep 5 165.53 11371 2121.6
## - writing_score:reading_score 1 12.47 11218 2121.6
## - parent_marital_status:transport_means 3 91.34 11297 2121.8
## - test_prep:wkly_study_hours 2 60.16 11266 2122.1
## - parent_educ:transport_means 5 175.32 11381 2122.1
## <none> 11205 2123.0
## - wkly_study_hours:writing_score 2 83.69 11289 2123.4
## - practice_sport:writing_score 2 85.78 11291 2123.5
## - ethnic_group:parent_educ 20 798.88 12004 2123.6
## - parent_marital_status:practice_sport 5 205.09 11410 2123.7
## - lunch_type:practice_sport 2 93.39 11299 2123.9
## - parent_educ:reading_score 5 209.40 11415 2123.9
## - practice_sport:reading_score 2 101.88 11307 2124.3
## - ethnic_group:writing_score 4 179.45 11385 2124.3
## - ethnic_group:reading_score 4 183.50 11389 2124.6
## - test_prep:parent_marital_status 3 154.76 11360 2125.1
## - parent_educ:lunch_type 5 237.66 11443 2125.3
## - parent_educ:writing_score 5 247.17 11452 2125.8
## - is_first_child:wkly_study_hours 2 135.04 11340 2126.0
## - parent_educ:is_first_child 5 266.59 11472 2126.8
## - ethnic_group:is_first_child 4 251.10 11456 2128.1
## - wkly_study_hours:reading_score 2 174.15 11380 2128.1
## + ethnic_group:practice_sport 8 179.30 11026 2129.4
## - test_prep:transport_means 1 163.77 11369 2129.5
## + ethnic_group:lunch_type 4 23.02 11182 2129.8
## + gender:parent_educ 5 57.64 11148 2129.9
## - lunch_type:is_first_child 1 174.65 11380 2130.1
## - is_first_child:transport_means 1 185.99 11391 2130.7
## + parent_educ:practice_sport 10 214.52 10991 2131.6
## + ethnic_group:wkly_study_hours 8 123.23 11082 2132.4
## + parent_educ:parent_marital_status 14 341.14 10864 2132.7
## + ethnic_group:parent_marital_status 11 192.32 11013 2134.8
##
## Step: AIC=2115
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:transport_means +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:transport_means 4 52.35 11488 2109.7
## - practice_sport:wkly_study_hours 4 54.01 11490 2109.8
## - parent_marital_status:is_first_child 3 16.54 11453 2109.9
## - parent_marital_status:reading_score 3 26.93 11463 2110.4
## - parent_marital_status:writing_score 3 32.31 11468 2110.7
## - gender:practice_sport 2 2.67 11439 2111.1
## - gender:wkly_study_hours 2 4.62 11441 2111.2
## - test_prep:practice_sport 2 11.63 11448 2111.6
## - gender:ethnic_group 4 90.60 11527 2111.7
## - gender:parent_marital_status 3 55.37 11492 2111.8
## - practice_sport:transport_means 2 19.82 11456 2112.0
## - transport_means:wkly_study_hours 2 20.22 11456 2112.0
## - ethnic_group:test_prep 4 100.86 11537 2112.2
## - practice_sport:is_first_child 2 23.61 11460 2112.2
## - parent_marital_status:wkly_study_hours 6 184.78 11621 2112.5
## - parent_marital_status:transport_means 3 68.39 11504 2112.5
## - lunch_type:parent_marital_status 2 36.35 11472 2112.9
## - parent_educ:lunch_type 5 155.03 11591 2112.9
## - lunch_type:reading_score 1 0.02 11436 2113.0
## - lunch_type:transport_means 1 0.08 11436 2113.0
## - transport_means:reading_score 1 0.42 11437 2113.0
## - lunch_type:writing_score 1 1.08 11437 2113.1
## - gender:reading_score 1 1.36 11438 2113.1
## - gender:lunch_type 1 1.45 11438 2113.1
## - gender:test_prep 1 1.61 11438 2113.1
## - gender:transport_means 1 1.84 11438 2113.1
## - test_prep:writing_score 1 2.20 11438 2113.1
## - is_first_child:writing_score 1 2.24 11438 2113.1
## - test_prep:wkly_study_hours 2 41.29 11477 2113.1
## - test_prep:is_first_child 1 2.70 11439 2113.1
## - test_prep:reading_score 1 4.88 11441 2113.2
## - parent_educ:test_prep 5 162.30 11598 2113.3
## - gender:is_first_child 1 6.36 11442 2113.3
## - wkly_study_hours:writing_score 2 46.01 11482 2113.4
## - transport_means:writing_score 1 7.18 11443 2113.4
## - lunch_type:test_prep 1 10.81 11447 2113.6
## - is_first_child:reading_score 1 11.16 11447 2113.6
## - parent_educ:transport_means 5 169.09 11605 2113.7
## - ethnic_group:parent_educ 20 778.97 12215 2113.9
## - writing_score:reading_score 1 17.40 11454 2113.9
## - gender:writing_score 1 23.31 11459 2114.2
## - practice_sport:writing_score 2 71.19 11507 2114.7
## - parent_marital_status:practice_sport 5 190.27 11626 2114.7
## - lunch_type:wkly_study_hours 2 74.79 11511 2114.8
## <none> 11436 2115.0
## - practice_sport:reading_score 2 79.80 11516 2115.1
## - parent_educ:reading_score 5 206.11 11642 2115.5
## - lunch_type:practice_sport 2 92.27 11528 2115.7
## - ethnic_group:reading_score 4 174.40 11610 2115.9
## - ethnic_group:writing_score 4 176.12 11612 2116.0
## - parent_educ:writing_score 5 221.50 11658 2116.3
## - is_first_child:wkly_study_hours 2 110.02 11546 2116.7
## - wkly_study_hours:reading_score 2 123.52 11560 2117.3
## - test_prep:parent_marital_status 3 165.15 11601 2117.5
## - parent_educ:is_first_child 5 253.03 11689 2117.9
## - ethnic_group:is_first_child 4 239.94 11676 2119.2
## - test_prep:transport_means 1 153.18 11589 2120.8
## - is_first_child:transport_means 1 167.96 11604 2121.6
## + ethnic_group:lunch_type 4 21.00 11415 2121.9
## + parent_educ:wkly_study_hours 10 230.83 11205 2123.0
## + gender:parent_educ 5 38.20 11398 2123.0
## + ethnic_group:practice_sport 8 152.49 11284 2123.1
## - lunch_type:is_first_child 1 211.45 11648 2123.8
## + parent_educ:practice_sport 10 193.99 11242 2124.9
## + parent_educ:parent_marital_status 14 328.12 11108 2125.8
## + ethnic_group:parent_marital_status 11 208.81 11227 2126.1
## + ethnic_group:wkly_study_hours 8 77.96 11358 2127.0
##
## Step: AIC=2109.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 56.16 11545 2104.6
## - parent_marital_status:is_first_child 3 19.14 11508 2104.7
## - parent_marital_status:reading_score 3 29.62 11518 2105.2
## - parent_marital_status:writing_score 3 35.02 11524 2105.5
## - gender:practice_sport 2 3.44 11492 2105.9
## - gender:wkly_study_hours 2 3.96 11492 2105.9
## - gender:parent_marital_status 3 49.54 11538 2106.2
## - test_prep:practice_sport 2 12.00 11500 2106.3
## - parent_marital_status:wkly_study_hours 6 171.23 11660 2106.4
## - gender:ethnic_group 4 92.92 11581 2106.4
## - parent_marital_status:transport_means 3 56.50 11545 2106.6
## - practice_sport:is_first_child 2 17.93 11506 2106.6
## - practice_sport:transport_means 2 18.20 11507 2106.6
## - transport_means:wkly_study_hours 2 27.28 11516 2107.1
## - lunch_type:parent_marital_status 2 33.00 11522 2107.4
## - lunch_type:transport_means 1 0.01 11488 2107.7
## - ethnic_group:test_prep 4 117.50 11606 2107.7
## - lunch_type:reading_score 1 0.23 11489 2107.7
## - gender:lunch_type 1 0.25 11489 2107.7
## - test_prep:writing_score 1 0.45 11489 2107.7
## - gender:reading_score 1 1.11 11490 2107.8
## - gender:transport_means 1 1.51 11490 2107.8
## - transport_means:reading_score 1 1.80 11490 2107.8
## - lunch_type:writing_score 1 1.85 11490 2107.8
## - test_prep:reading_score 1 2.13 11491 2107.8
## - parent_educ:transport_means 5 159.05 11648 2107.8
## - gender:test_prep 1 2.48 11491 2107.8
## - parent_educ:test_prep 5 160.44 11649 2107.9
## - test_prep:wkly_study_hours 2 42.98 11532 2107.9
## - transport_means:writing_score 1 3.98 11492 2107.9
## - test_prep:is_first_child 1 4.41 11493 2107.9
## - is_first_child:writing_score 1 5.20 11494 2108.0
## - gender:is_first_child 1 6.16 11495 2108.0
## - wkly_study_hours:writing_score 2 48.70 11537 2108.2
## - parent_educ:lunch_type 5 167.65 11656 2108.2
## - writing_score:reading_score 1 13.50 11502 2108.4
## - lunch_type:test_prep 1 14.35 11503 2108.4
## - is_first_child:reading_score 1 17.58 11506 2108.6
## - ethnic_group:parent_educ 20 787.62 12276 2108.8
## - gender:writing_score 1 24.28 11513 2108.9
## - lunch_type:wkly_study_hours 2 70.36 11559 2109.3
## - parent_marital_status:practice_sport 5 189.71 11678 2109.4
## - parent_educ:reading_score 5 195.94 11684 2109.7
## <none> 11488 2109.7
## - practice_sport:writing_score 2 78.54 11567 2109.7
## - practice_sport:reading_score 2 88.67 11577 2110.2
## - parent_educ:writing_score 5 212.17 11701 2110.5
## - is_first_child:wkly_study_hours 2 103.37 11592 2111.0
## - lunch_type:practice_sport 2 104.84 11593 2111.1
## - ethnic_group:reading_score 4 186.85 11675 2111.2
## - ethnic_group:writing_score 4 189.57 11678 2111.3
## - test_prep:parent_marital_status 3 162.30 11651 2112.0
## - wkly_study_hours:reading_score 2 129.77 11618 2112.3
## - parent_educ:is_first_child 5 250.08 11739 2112.4
## - ethnic_group:is_first_child 4 245.84 11734 2114.2
## + ethnic_group:transport_means 4 52.35 11436 2115.0
## - test_prep:transport_means 1 146.39 11635 2115.2
## - is_first_child:transport_means 1 165.15 11654 2116.1
## + ethnic_group:lunch_type 4 25.77 11463 2116.4
## + gender:parent_educ 5 34.75 11454 2117.9
## + ethnic_group:practice_sport 8 147.41 11341 2118.1
## + parent_educ:wkly_study_hours 10 217.73 11271 2118.4
## - lunch_type:is_first_child 1 214.06 11702 2118.6
## + parent_educ:practice_sport 10 211.18 11277 2118.8
## + ethnic_group:parent_marital_status 11 218.43 11270 2120.4
## + parent_educ:parent_marital_status 14 316.32 11172 2121.2
## + ethnic_group:wkly_study_hours 8 74.34 11414 2121.9
##
## Step: AIC=2104.57
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:reading_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:is_first_child 3 18.64 11563 2099.5
## - parent_marital_status:wkly_study_hours 6 154.99 11700 2100.4
## - parent_marital_status:reading_score 3 40.15 11585 2100.6
## - parent_marital_status:transport_means 3 40.94 11586 2100.7
## - gender:wkly_study_hours 2 2.89 11548 2100.7
## - parent_marital_status:writing_score 3 46.61 11591 2100.9
## - gender:practice_sport 2 8.86 11554 2101.0
## - gender:ethnic_group 4 88.58 11633 2101.1
## - test_prep:practice_sport 2 11.67 11556 2101.2
## - gender:parent_marital_status 3 53.78 11598 2101.3
## - ethnic_group:parent_educ 20 745.11 12290 2101.5
## - practice_sport:is_first_child 2 18.65 11563 2101.5
## - practice_sport:transport_means 2 19.02 11564 2101.6
## - transport_means:wkly_study_hours 2 19.75 11564 2101.6
## - parent_educ:test_prep 5 149.37 11694 2102.2
## - ethnic_group:test_prep 4 113.10 11658 2102.3
## - lunch_type:parent_marital_status 2 36.59 11581 2102.4
## - lunch_type:transport_means 1 0.03 11545 2102.6
## - lunch_type:reading_score 1 0.33 11545 2102.6
## - gender:lunch_type 1 0.55 11545 2102.6
## - gender:transport_means 1 0.67 11545 2102.6
## - test_prep:writing_score 1 0.89 11546 2102.6
## - gender:reading_score 1 1.15 11546 2102.6
## - transport_means:reading_score 1 1.56 11546 2102.7
## - lunch_type:writing_score 1 1.97 11547 2102.7
## - test_prep:is_first_child 1 1.98 11547 2102.7
## - gender:test_prep 1 1.99 11547 2102.7
## - parent_educ:transport_means 5 159.65 11704 2102.7
## - test_prep:reading_score 1 2.52 11547 2102.7
## - test_prep:wkly_study_hours 2 41.99 11587 2102.7
## - is_first_child:writing_score 1 3.58 11548 2102.8
## - transport_means:writing_score 1 4.63 11549 2102.8
## - gender:is_first_child 1 5.24 11550 2102.8
## - lunch_type:test_prep 1 9.92 11555 2103.1
## - parent_educ:lunch_type 5 171.28 11716 2103.3
## - writing_score:reading_score 1 14.72 11559 2103.3
## - wkly_study_hours:writing_score 2 55.18 11600 2103.4
## - is_first_child:reading_score 1 16.11 11561 2103.4
## - parent_educ:reading_score 5 183.39 11728 2103.9
## - gender:writing_score 1 25.52 11570 2103.9
## - parent_marital_status:practice_sport 5 185.07 11730 2104.0
## - lunch_type:wkly_study_hours 2 67.58 11612 2104.0
## <none> 11545 2104.6
## - practice_sport:writing_score 2 80.97 11626 2104.7
## - parent_educ:writing_score 5 200.47 11745 2104.7
## - practice_sport:reading_score 2 89.10 11634 2105.1
## - ethnic_group:reading_score 4 170.74 11715 2105.2
## - ethnic_group:writing_score 4 175.80 11720 2105.5
## - lunch_type:practice_sport 2 101.07 11646 2105.7
## - is_first_child:wkly_study_hours 2 105.32 11650 2105.9
## - test_prep:parent_marital_status 3 154.65 11699 2106.4
## - parent_educ:is_first_child 5 237.09 11782 2106.6
## - wkly_study_hours:reading_score 2 145.17 11690 2107.9
## - ethnic_group:is_first_child 4 246.91 11792 2109.1
## - test_prep:transport_means 1 139.51 11684 2109.7
## + practice_sport:wkly_study_hours 4 56.16 11488 2109.7
## + ethnic_group:transport_means 4 54.50 11490 2109.8
## + ethnic_group:lunch_type 4 23.53 11521 2111.4
## - is_first_child:transport_means 1 175.41 11720 2111.5
## - lunch_type:is_first_child 1 193.31 11738 2112.4
## + parent_educ:wkly_study_hours 10 225.81 11319 2112.9
## + gender:parent_educ 5 31.18 11514 2113.0
## + parent_educ:practice_sport 10 223.69 11321 2113.0
## + ethnic_group:practice_sport 8 141.96 11403 2113.3
## + ethnic_group:parent_marital_status 11 223.08 11322 2115.1
## + parent_educ:parent_marital_status 14 323.97 11221 2115.8
## + ethnic_group:wkly_study_hours 8 72.25 11472 2116.9
##
## Step: AIC=2099.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## parent_marital_status:reading_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:reading_score 3 37.94 11601 2095.5
## - gender:wkly_study_hours 2 1.56 11565 2095.6
## - parent_marital_status:writing_score 3 40.91 11604 2095.6
## - gender:practice_sport 2 8.86 11572 2096.0
## - test_prep:practice_sport 2 9.47 11573 2096.0
## - gender:ethnic_group 4 89.11 11652 2096.1
## - ethnic_group:parent_educ 20 745.94 12309 2096.4
## - parent_marital_status:transport_means 3 58.11 11621 2096.5
## - practice_sport:transport_means 2 19.92 11583 2096.5
## - transport_means:wkly_study_hours 2 20.64 11584 2096.6
## - practice_sport:is_first_child 2 22.99 11586 2096.7
## - parent_marital_status:wkly_study_hours 6 184.33 11748 2096.9
## - parent_educ:test_prep 5 149.70 11713 2097.1
## - lunch_type:parent_marital_status 2 37.84 11601 2097.4
## - lunch_type:transport_means 1 0.00 11563 2097.5
## - gender:transport_means 1 0.49 11564 2097.6
## - ethnic_group:test_prep 4 118.75 11682 2097.6
## - lunch_type:reading_score 1 0.75 11564 2097.6
## - test_prep:writing_score 1 0.95 11564 2097.6
## - gender:reading_score 1 1.13 11564 2097.6
## - gender:lunch_type 1 1.21 11564 2097.6
## - gender:test_prep 1 1.34 11565 2097.6
## - transport_means:reading_score 1 1.64 11565 2097.6
## - test_prep:is_first_child 1 2.27 11566 2097.6
## - test_prep:reading_score 1 2.53 11566 2097.7
## - lunch_type:writing_score 1 2.60 11566 2097.7
## - test_prep:wkly_study_hours 2 42.69 11606 2097.7
## - parent_educ:lunch_type 5 161.67 11725 2097.7
## - is_first_child:writing_score 1 4.10 11567 2097.7
## - transport_means:writing_score 1 4.85 11568 2097.8
## - gender:is_first_child 1 6.08 11569 2097.8
## - lunch_type:test_prep 1 8.34 11572 2097.9
## - writing_score:reading_score 1 14.24 11578 2098.2
## - parent_educ:transport_means 5 172.34 11736 2098.2
## - wkly_study_hours:writing_score 2 54.80 11618 2098.3
## - is_first_child:reading_score 1 18.57 11582 2098.5
## - parent_educ:reading_score 5 178.06 11741 2098.5
## - gender:writing_score 1 24.52 11588 2098.8
## - gender:parent_marital_status 3 105.47 11669 2098.9
## - lunch_type:wkly_study_hours 2 70.19 11634 2099.1
## - parent_marital_status:practice_sport 5 191.26 11754 2099.2
## - parent_educ:writing_score 5 193.51 11757 2099.3
## <none> 11563 2099.5
## - practice_sport:writing_score 2 82.36 11646 2099.7
## - practice_sport:reading_score 2 89.45 11653 2100.1
## - ethnic_group:reading_score 4 170.41 11734 2100.2
## - ethnic_group:writing_score 4 175.89 11739 2100.4
## - lunch_type:practice_sport 2 96.71 11660 2100.4
## - parent_educ:is_first_child 5 235.26 11798 2101.4
## - is_first_child:wkly_study_hours 2 120.77 11684 2101.7
## - test_prep:parent_marital_status 3 162.52 11726 2101.8
## - wkly_study_hours:reading_score 2 145.19 11708 2102.9
## - ethnic_group:is_first_child 4 249.85 11813 2104.1
## - test_prep:transport_means 1 137.93 11701 2104.5
## + parent_marital_status:is_first_child 3 18.64 11545 2104.6
## + ethnic_group:transport_means 4 56.96 11506 2104.6
## + practice_sport:wkly_study_hours 4 55.66 11508 2104.7
## + ethnic_group:lunch_type 4 21.03 11542 2106.4
## - is_first_child:transport_means 1 191.03 11754 2107.2
## - lunch_type:is_first_child 1 196.21 11760 2107.4
## + gender:parent_educ 5 28.74 11534 2108.1
## + parent_educ:practice_sport 10 220.48 11343 2108.2
## + parent_educ:wkly_study_hours 10 216.00 11347 2108.4
## + ethnic_group:practice_sport 8 136.76 11426 2108.5
## + ethnic_group:parent_marital_status 11 218.20 11345 2110.3
## + ethnic_group:wkly_study_hours 8 68.51 11495 2112.0
## + parent_educ:parent_marital_status 15 331.78 11232 2112.3
##
## Step: AIC=2095.46
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:writing_score 3 14.06 11615 2090.2
## - gender:wkly_study_hours 2 2.17 11603 2091.6
## - gender:ethnic_group 4 85.71 11687 2091.8
## - gender:practice_sport 2 9.38 11611 2091.9
## - test_prep:practice_sport 2 11.09 11612 2092.0
## - ethnic_group:parent_educ 20 744.19 12345 2092.1
## - practice_sport:transport_means 2 15.66 11617 2092.2
## - parent_marital_status:transport_means 3 55.37 11657 2092.3
## - practice_sport:is_first_child 2 19.31 11620 2092.4
## - parent_marital_status:wkly_study_hours 6 178.85 11780 2092.5
## - transport_means:wkly_study_hours 2 22.41 11624 2092.6
## - parent_educ:test_prep 5 147.26 11748 2092.9
## - lunch_type:parent_marital_status 2 37.74 11639 2093.4
## - test_prep:wkly_study_hours 2 38.75 11640 2093.4
## - ethnic_group:test_prep 4 118.79 11720 2093.5
## - lunch_type:transport_means 1 0.40 11602 2093.5
## - lunch_type:reading_score 1 0.56 11602 2093.5
## - test_prep:writing_score 1 0.65 11602 2093.5
## - gender:lunch_type 1 0.70 11602 2093.5
## - gender:reading_score 1 0.88 11602 2093.5
## - test_prep:reading_score 1 1.77 11603 2093.6
## - gender:test_prep 1 1.89 11603 2093.6
## - transport_means:reading_score 1 2.10 11603 2093.6
## - lunch_type:writing_score 1 2.30 11604 2093.6
## - gender:transport_means 1 2.46 11604 2093.6
## - is_first_child:writing_score 1 3.51 11605 2093.6
## - parent_educ:lunch_type 5 162.06 11763 2093.6
## - test_prep:is_first_child 1 4.08 11605 2093.7
## - transport_means:writing_score 1 4.82 11606 2093.7
## - gender:is_first_child 1 5.35 11607 2093.7
## - wkly_study_hours:writing_score 2 44.97 11646 2093.7
## - lunch_type:test_prep 1 7.15 11608 2093.8
## - writing_score:reading_score 1 16.47 11618 2094.3
## - is_first_child:reading_score 1 17.24 11618 2094.3
## - parent_educ:reading_score 5 177.65 11779 2094.4
## - parent_marital_status:practice_sport 5 179.16 11780 2094.5
## - gender:writing_score 1 23.44 11625 2094.7
## - gender:parent_marital_status 3 103.77 11705 2094.7
## - lunch_type:wkly_study_hours 2 65.57 11667 2094.8
## - parent_educ:transport_means 5 189.84 11791 2095.0
## - parent_educ:writing_score 5 190.36 11792 2095.1
## <none> 11601 2095.5
## - practice_sport:writing_score 2 82.85 11684 2095.7
## - practice_sport:reading_score 2 95.57 11697 2096.3
## - ethnic_group:reading_score 4 182.96 11784 2096.7
## - ethnic_group:writing_score 4 188.32 11790 2097.0
## - lunch_type:practice_sport 2 113.33 11715 2097.2
## - parent_educ:is_first_child 5 236.26 11838 2097.3
## - test_prep:parent_marital_status 3 158.72 11760 2097.5
## - is_first_child:wkly_study_hours 2 121.09 11722 2097.6
## - wkly_study_hours:reading_score 2 131.21 11732 2098.1
## + parent_marital_status:reading_score 3 37.94 11563 2099.5
## + practice_sport:wkly_study_hours 4 64.78 11536 2100.2
## - ethnic_group:is_first_child 4 253.99 11855 2100.2
## - test_prep:transport_means 1 138.45 11740 2100.5
## + ethnic_group:transport_means 4 57.10 11544 2100.6
## + parent_marital_status:is_first_child 3 16.43 11585 2100.6
## + ethnic_group:lunch_type 4 21.38 11580 2102.4
## - lunch_type:is_first_child 1 195.87 11797 2103.3
## - is_first_child:transport_means 1 197.63 11799 2103.4
## + gender:parent_educ 5 24.55 11577 2104.2
## + ethnic_group:practice_sport 8 136.95 11464 2104.4
## + parent_educ:wkly_study_hours 10 210.88 11390 2104.6
## + parent_educ:practice_sport 10 194.67 11407 2105.5
## + ethnic_group:parent_marital_status 11 222.81 11378 2106.0
## + ethnic_group:wkly_study_hours 8 72.84 11528 2107.7
## + parent_educ:parent_marital_status 15 246.29 11355 2112.8
##
## Step: AIC=2090.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:wkly_study_hours 2 1.90 11617 2086.3
## - gender:ethnic_group 4 85.99 11701 2086.5
## - gender:practice_sport 2 9.40 11625 2086.7
## - ethnic_group:parent_educ 20 742.41 12358 2086.7
## - test_prep:practice_sport 2 11.44 11627 2086.8
## - parent_marital_status:transport_means 3 51.32 11667 2086.8
## - practice_sport:transport_means 2 13.53 11629 2086.9
## - practice_sport:is_first_child 2 20.48 11636 2087.2
## - parent_educ:test_prep 5 139.91 11755 2087.2
## - transport_means:wkly_study_hours 2 22.45 11638 2087.3
## - parent_marital_status:wkly_study_hours 6 191.78 11807 2087.8
## - test_prep:wkly_study_hours 2 39.62 11655 2088.2
## - lunch_type:transport_means 1 0.27 11616 2088.2
## - lunch_type:reading_score 1 0.46 11616 2088.2
## - gender:lunch_type 1 0.72 11616 2088.2
## - test_prep:writing_score 1 0.77 11616 2088.2
## - gender:reading_score 1 1.27 11617 2088.2
## - ethnic_group:test_prep 4 120.10 11735 2088.2
## - transport_means:reading_score 1 1.70 11617 2088.3
## - test_prep:reading_score 1 1.71 11617 2088.3
## - gender:transport_means 1 2.20 11618 2088.3
## - gender:test_prep 1 2.31 11618 2088.3
## - lunch_type:writing_score 1 2.33 11618 2088.3
## - lunch_type:parent_marital_status 2 43.27 11659 2088.4
## - test_prep:is_first_child 1 4.07 11619 2088.4
## - is_first_child:writing_score 1 4.17 11620 2088.4
## - transport_means:writing_score 1 5.08 11620 2088.4
## - gender:is_first_child 1 5.66 11621 2088.5
## - wkly_study_hours:writing_score 2 45.32 11661 2088.5
## - lunch_type:test_prep 1 6.55 11622 2088.5
## - parent_educ:lunch_type 5 168.67 11784 2088.7
## - is_first_child:reading_score 1 18.65 11634 2089.1
## - gender:parent_marital_status 3 98.91 11714 2089.2
## - parent_educ:reading_score 5 180.15 11795 2089.2
## - writing_score:reading_score 1 22.76 11638 2089.3
## - gender:writing_score 1 24.71 11640 2089.4
## - lunch_type:wkly_study_hours 2 64.45 11680 2089.4
## - parent_marital_status:practice_sport 5 188.37 11804 2089.7
## - parent_educ:transport_means 5 189.17 11804 2089.7
## - parent_educ:writing_score 5 192.00 11807 2089.8
## <none> 11615 2090.2
## - practice_sport:writing_score 2 79.49 11695 2090.2
## - practice_sport:reading_score 2 94.16 11709 2090.9
## - parent_educ:is_first_child 5 227.45 11843 2091.6
## - ethnic_group:reading_score 4 195.00 11810 2092.0
## - lunch_type:practice_sport 2 116.92 11732 2092.1
## - is_first_child:wkly_study_hours 2 122.20 11738 2092.3
## - ethnic_group:writing_score 4 202.51 11818 2092.4
## - wkly_study_hours:reading_score 2 131.21 11746 2092.8
## - test_prep:parent_marital_status 3 175.70 11791 2093.0
## + practice_sport:wkly_study_hours 4 64.72 11551 2094.9
## - ethnic_group:is_first_child 4 257.50 11873 2095.1
## - test_prep:transport_means 1 137.72 11753 2095.1
## + ethnic_group:transport_means 4 55.50 11560 2095.3
## + parent_marital_status:is_first_child 3 15.57 11600 2095.4
## + parent_marital_status:writing_score 3 14.06 11601 2095.5
## + parent_marital_status:reading_score 3 11.09 11604 2095.6
## + ethnic_group:lunch_type 4 20.25 11595 2097.1
## - lunch_type:is_first_child 1 198.08 11813 2098.2
## - is_first_child:transport_means 1 203.38 11819 2098.4
## + gender:parent_educ 5 24.08 11591 2098.9
## + parent_educ:wkly_study_hours 10 214.51 11401 2099.2
## + ethnic_group:practice_sport 8 136.47 11479 2099.2
## + parent_educ:practice_sport 10 198.09 11417 2100.0
## + ethnic_group:parent_marital_status 11 198.75 11416 2102.0
## + ethnic_group:wkly_study_hours 8 71.66 11544 2102.5
## + parent_educ:parent_marital_status 15 233.46 11382 2108.2
##
## Step: AIC=2086.27
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:ethnic_group + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 85.24 11702 2082.6
## - gender:practice_sport 2 9.72 11627 2082.8
## - test_prep:practice_sport 2 11.38 11629 2082.8
## - parent_marital_status:transport_means 3 51.56 11669 2082.9
## - practice_sport:transport_means 2 13.98 11631 2083.0
## - ethnic_group:parent_educ 20 752.15 12369 2083.3
## - practice_sport:is_first_child 2 20.96 11638 2083.3
## - parent_educ:test_prep 5 140.26 11758 2083.3
## - transport_means:wkly_study_hours 2 22.93 11640 2083.4
## - lunch_type:transport_means 1 0.25 11617 2084.3
## - lunch_type:reading_score 1 0.35 11618 2084.3
## - test_prep:writing_score 1 0.64 11618 2084.3
## - gender:lunch_type 1 0.84 11618 2084.3
## - gender:reading_score 1 1.36 11619 2084.3
## - test_prep:reading_score 1 1.54 11619 2084.3
## - transport_means:reading_score 1 1.65 11619 2084.3
## - lunch_type:writing_score 1 2.13 11619 2084.4
## - gender:transport_means 1 2.22 11619 2084.4
## - test_prep:wkly_study_hours 2 41.82 11659 2084.4
## - gender:test_prep 1 2.73 11620 2084.4
## - ethnic_group:test_prep 4 121.51 11739 2084.4
## - lunch_type:parent_marital_status 2 42.23 11659 2084.4
## - parent_marital_status:wkly_study_hours 6 202.30 11820 2084.5
## - test_prep:is_first_child 1 3.97 11621 2084.5
## - is_first_child:writing_score 1 4.73 11622 2084.5
## - transport_means:writing_score 1 5.27 11622 2084.5
## - gender:is_first_child 1 5.85 11623 2084.6
## - lunch_type:test_prep 1 6.82 11624 2084.6
## - parent_educ:lunch_type 5 167.40 11785 2084.7
## - wkly_study_hours:writing_score 2 53.00 11670 2085.0
## - is_first_child:reading_score 1 20.01 11637 2085.3
## - writing_score:reading_score 1 22.76 11640 2085.4
## - parent_educ:reading_score 5 182.22 11799 2085.4
## - lunch_type:wkly_study_hours 2 63.49 11681 2085.5
## - gender:parent_marital_status 3 103.73 11721 2085.5
## - gender:writing_score 1 24.84 11642 2085.5
## - parent_marital_status:practice_sport 5 190.33 11808 2085.9
## - parent_educ:transport_means 5 190.61 11808 2085.9
## - parent_educ:writing_score 5 193.69 11811 2086.0
## <none> 11617 2086.3
## - practice_sport:writing_score 2 80.44 11698 2086.3
## - practice_sport:reading_score 2 94.22 11711 2087.0
## - parent_educ:is_first_child 5 225.69 11843 2087.6
## - ethnic_group:reading_score 4 195.64 11813 2088.1
## - lunch_type:practice_sport 2 119.86 11737 2088.3
## - is_first_child:wkly_study_hours 2 122.02 11739 2088.4
## - ethnic_group:writing_score 4 203.54 11821 2088.5
## - test_prep:parent_marital_status 3 174.80 11792 2089.1
## - wkly_study_hours:reading_score 2 140.79 11758 2089.4
## + gender:wkly_study_hours 2 1.90 11615 2090.2
## + practice_sport:wkly_study_hours 4 63.46 11554 2091.0
## - test_prep:transport_means 1 139.76 11757 2091.3
## + ethnic_group:transport_means 4 54.95 11562 2091.5
## + parent_marital_status:is_first_child 3 14.10 11603 2091.6
## + parent_marital_status:writing_score 3 13.79 11603 2091.6
## - ethnic_group:is_first_child 4 267.25 11884 2091.7
## + parent_marital_status:reading_score 3 10.76 11606 2091.7
## + ethnic_group:lunch_type 4 20.71 11596 2093.2
## - lunch_type:is_first_child 1 198.87 11816 2094.3
## - is_first_child:transport_means 1 206.12 11823 2094.7
## + gender:parent_educ 5 24.16 11593 2095.0
## + parent_educ:wkly_study_hours 10 216.08 11401 2095.2
## + ethnic_group:practice_sport 8 135.85 11481 2095.3
## + parent_educ:practice_sport 10 194.10 11423 2096.3
## + ethnic_group:parent_marital_status 11 198.17 11419 2098.1
## + ethnic_group:wkly_study_hours 8 72.34 11545 2098.6
## + parent_educ:parent_marital_status 15 231.61 11386 2104.4
##
## Step: AIC=2082.58
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 8.04 11710 2079.0
## - test_prep:practice_sport 2 8.95 11711 2079.0
## - gender:practice_sport 2 11.76 11714 2079.2
## - parent_marital_status:transport_means 3 56.96 11759 2079.4
## - transport_means:wkly_study_hours 2 22.02 11724 2079.7
## - practice_sport:is_first_child 2 23.29 11726 2079.8
## - lunch_type:parent_marital_status 2 35.54 11738 2080.4
## - parent_educ:test_prep 5 155.61 11858 2080.4
## - ethnic_group:test_prep 4 119.01 11821 2080.6
## - parent_marital_status:wkly_study_hours 6 200.11 11902 2080.6
## - gender:lunch_type 1 0.10 11702 2080.6
## - lunch_type:reading_score 1 0.18 11703 2080.6
## - lunch_type:transport_means 1 0.32 11703 2080.6
## - test_prep:writing_score 1 0.36 11703 2080.6
## - test_prep:reading_score 1 1.06 11704 2080.6
## - lunch_type:writing_score 1 1.41 11704 2080.7
## - gender:transport_means 1 2.31 11705 2080.7
## - test_prep:wkly_study_hours 2 42.36 11745 2080.7
## - gender:reading_score 1 3.01 11705 2080.7
## - transport_means:writing_score 1 3.19 11706 2080.7
## - parent_educ:reading_score 5 163.04 11866 2080.8
## - transport_means:reading_score 1 3.63 11706 2080.8
## - is_first_child:writing_score 1 4.25 11707 2080.8
## - gender:is_first_child 1 4.30 11707 2080.8
## - test_prep:is_first_child 1 4.43 11707 2080.8
## - gender:test_prep 1 4.66 11707 2080.8
## - lunch_type:test_prep 1 8.48 11711 2081.0
## - wkly_study_hours:writing_score 2 49.96 11752 2081.1
## - ethnic_group:parent_educ 20 790.68 12493 2081.2
## - parent_educ:transport_means 5 175.76 11878 2081.4
## - parent_educ:lunch_type 5 175.76 11878 2081.4
## - is_first_child:reading_score 1 19.36 11722 2081.6
## - parent_educ:writing_score 5 181.85 11884 2081.7
## - writing_score:reading_score 1 21.84 11724 2081.7
## - lunch_type:wkly_study_hours 2 63.06 11766 2081.8
## - gender:parent_marital_status 3 108.51 11811 2082.0
## - gender:writing_score 1 33.87 11736 2082.3
## <none> 11702 2082.6
## - parent_marital_status:practice_sport 5 203.21 11906 2082.7
## - ethnic_group:reading_score 4 167.13 11870 2082.9
## - ethnic_group:writing_score 4 168.87 11871 2083.0
## - practice_sport:writing_score 2 89.06 11792 2083.1
## - practice_sport:reading_score 2 99.46 11802 2083.6
## - is_first_child:wkly_study_hours 2 121.58 11824 2084.7
## - parent_educ:is_first_child 5 247.68 11950 2084.9
## - lunch_type:practice_sport 2 128.62 11831 2085.0
## - test_prep:parent_marital_status 3 174.47 11877 2085.3
## - wkly_study_hours:reading_score 2 138.29 11841 2085.5
## + gender:ethnic_group 4 85.24 11617 2086.3
## + gender:wkly_study_hours 2 1.15 11701 2086.5
## + ethnic_group:transport_means 4 60.36 11642 2087.5
## + practice_sport:wkly_study_hours 4 59.57 11643 2087.6
## - test_prep:transport_means 1 144.46 11847 2087.8
## + parent_marital_status:is_first_child 3 14.30 11688 2087.9
## + parent_marital_status:writing_score 3 13.99 11688 2087.9
## + parent_marital_status:reading_score 3 11.19 11691 2088.0
## - ethnic_group:is_first_child 4 282.33 11985 2088.7
## + ethnic_group:lunch_type 4 30.48 11672 2089.0
## - lunch_type:is_first_child 1 211.76 11914 2091.2
## + gender:parent_educ 5 17.96 11684 2091.7
## - is_first_child:transport_means 1 225.28 11928 2091.8
## + ethnic_group:practice_sport 8 132.88 11570 2091.8
## + parent_educ:wkly_study_hours 10 207.02 11495 2092.1
## + parent_educ:practice_sport 10 195.61 11507 2092.6
## + ethnic_group:parent_marital_status 11 206.85 11496 2094.1
## + ethnic_group:wkly_study_hours 8 80.69 11622 2094.5
## + parent_educ:parent_marital_status 15 226.68 11476 2101.0
##
## Step: AIC=2078.99
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:reading_score +
## parent_marital_status:practice_sport + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 9.71 11720 2075.5
## - gender:practice_sport 2 13.24 11724 2075.7
## - parent_marital_status:transport_means 3 58.27 11769 2075.9
## - transport_means:wkly_study_hours 2 21.83 11732 2076.1
## - practice_sport:is_first_child 2 22.58 11733 2076.1
## - lunch_type:parent_marital_status 2 35.22 11746 2076.8
## - ethnic_group:test_prep 4 117.57 11828 2076.9
## - parent_educ:reading_score 5 158.06 11868 2076.9
## - parent_marital_status:wkly_study_hours 6 200.13 11911 2077.0
## - gender:lunch_type 1 0.07 11710 2077.0
## - lunch_type:reading_score 1 0.16 11711 2077.0
## - lunch_type:transport_means 1 0.25 11711 2077.0
## - test_prep:writing_score 1 0.53 11711 2077.0
## - parent_educ:test_prep 5 160.69 11871 2077.0
## - lunch_type:writing_score 1 1.26 11712 2077.1
## - test_prep:reading_score 1 1.35 11712 2077.1
## - gender:transport_means 1 2.23 11713 2077.1
## - transport_means:writing_score 1 2.34 11713 2077.1
## - gender:reading_score 1 3.06 11714 2077.1
## - is_first_child:writing_score 1 3.79 11714 2077.2
## - test_prep:is_first_child 1 4.04 11714 2077.2
## - gender:is_first_child 1 4.57 11715 2077.2
## - gender:test_prep 1 5.05 11716 2077.2
## - transport_means:reading_score 1 5.07 11716 2077.2
## - test_prep:wkly_study_hours 2 46.18 11757 2077.3
## - lunch_type:test_prep 1 9.03 11720 2077.4
## - wkly_study_hours:writing_score 2 50.83 11761 2077.5
## - parent_educ:transport_means 5 172.56 11883 2077.6
## - parent_educ:writing_score 5 177.42 11888 2077.9
## - is_first_child:reading_score 1 18.85 11729 2077.9
## - parent_educ:lunch_type 5 179.63 11890 2078.0
## - writing_score:reading_score 1 21.45 11732 2078.1
## - lunch_type:wkly_study_hours 2 61.81 11772 2078.1
## - gender:parent_marital_status 3 105.08 11816 2078.3
## - gender:writing_score 1 34.65 11745 2078.7
## <none> 11710 2079.0
## - parent_marital_status:practice_sport 5 202.74 11913 2079.1
## - ethnic_group:parent_educ 20 825.22 12536 2079.2
## - ethnic_group:reading_score 4 167.15 11878 2079.3
## - ethnic_group:writing_score 4 168.01 11878 2079.4
## - practice_sport:writing_score 2 91.15 11802 2079.6
## - practice_sport:reading_score 2 102.47 11813 2080.1
## - is_first_child:wkly_study_hours 2 123.13 11834 2081.2
## - parent_educ:is_first_child 5 251.54 11962 2081.5
## - lunch_type:practice_sport 2 131.95 11842 2081.6
## - test_prep:parent_marital_status 3 173.50 11884 2081.7
## - wkly_study_hours:reading_score 2 138.10 11849 2081.9
## + practice_sport:transport_means 2 8.04 11702 2082.6
## + gender:wkly_study_hours 2 1.33 11709 2082.9
## + gender:ethnic_group 4 79.30 11631 2083.0
## + practice_sport:wkly_study_hours 4 60.11 11650 2083.9
## + ethnic_group:transport_means 4 57.79 11653 2084.1
## - test_prep:transport_means 1 143.38 11854 2084.2
## + parent_marital_status:is_first_child 3 15.82 11695 2084.2
## + parent_marital_status:writing_score 3 12.30 11698 2084.4
## + parent_marital_status:reading_score 3 9.82 11701 2084.5
## - ethnic_group:is_first_child 4 278.94 11989 2084.9
## + ethnic_group:lunch_type 4 27.32 11683 2085.6
## - lunch_type:is_first_child 1 208.17 11919 2087.4
## + gender:parent_educ 5 18.25 11692 2088.1
## + ethnic_group:practice_sport 8 130.82 11580 2088.4
## + parent_educ:wkly_study_hours 10 207.46 11503 2088.4
## - is_first_child:transport_means 1 234.59 11945 2088.7
## + parent_educ:practice_sport 10 192.14 11518 2089.2
## + ethnic_group:wkly_study_hours 8 85.60 11625 2090.7
## + ethnic_group:parent_marital_status 11 202.22 11508 2090.7
## + parent_educ:parent_marital_status 15 229.78 11481 2097.3
##
## Step: AIC=2075.48
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:transport_means +
## gender:writing_score + gender:reading_score + ethnic_group:parent_educ +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:practice_sport 2 11.70 11732 2072.1
## - parent_marital_status:transport_means 3 57.34 11778 2072.4
## - practice_sport:is_first_child 2 20.00 11740 2072.5
## - transport_means:wkly_study_hours 2 20.64 11741 2072.5
## - ethnic_group:test_prep 4 114.46 11835 2073.2
## - lunch_type:parent_marital_status 2 34.55 11755 2073.2
## - parent_educ:reading_score 5 156.39 11877 2073.3
## - parent_educ:test_prep 5 157.07 11877 2073.3
## - gender:lunch_type 1 0.04 11720 2073.5
## - lunch_type:transport_means 1 0.17 11720 2073.5
## - lunch_type:reading_score 1 0.34 11720 2073.5
## - parent_marital_status:wkly_study_hours 6 200.89 11921 2073.5
## - lunch_type:writing_score 1 1.63 11722 2073.6
## - transport_means:writing_score 1 1.98 11722 2073.6
## - gender:transport_means 1 2.20 11722 2073.6
## - test_prep:writing_score 1 2.24 11722 2073.6
## - gender:reading_score 1 3.34 11724 2073.7
## - test_prep:reading_score 1 3.45 11724 2073.7
## - is_first_child:writing_score 1 3.80 11724 2073.7
## - gender:test_prep 1 4.16 11724 2073.7
## - gender:is_first_child 1 4.49 11725 2073.7
## - test_prep:is_first_child 1 4.60 11725 2073.7
## - transport_means:reading_score 1 5.64 11726 2073.8
## - test_prep:wkly_study_hours 2 46.32 11766 2073.8
## - lunch_type:test_prep 1 8.18 11728 2073.9
## - parent_educ:transport_means 5 169.82 11890 2074.0
## - wkly_study_hours:writing_score 2 50.44 11771 2074.0
## - parent_educ:writing_score 5 174.72 11895 2074.2
## - parent_educ:lunch_type 5 178.56 11899 2074.4
## - is_first_child:reading_score 1 19.11 11739 2074.4
## - writing_score:reading_score 1 19.87 11740 2074.5
## - lunch_type:wkly_study_hours 2 62.66 11783 2074.6
## - gender:parent_marital_status 3 105.20 11825 2074.8
## - gender:writing_score 1 35.28 11756 2075.2
## <none> 11720 2075.5
## - ethnic_group:reading_score 4 161.27 11882 2075.5
## - ethnic_group:writing_score 4 162.95 11883 2075.6
## - parent_marital_status:practice_sport 5 206.37 11927 2075.8
## - ethnic_group:parent_educ 20 836.92 12557 2076.2
## - practice_sport:writing_score 2 109.89 11830 2077.0
## - practice_sport:reading_score 2 111.20 11831 2077.1
## - is_first_child:wkly_study_hours 2 121.95 11842 2077.6
## - parent_educ:is_first_child 5 249.39 11970 2077.9
## - test_prep:parent_marital_status 3 169.22 11889 2077.9
## - wkly_study_hours:reading_score 2 137.85 11858 2078.4
## - lunch_type:practice_sport 2 145.62 11866 2078.8
## + test_prep:practice_sport 2 9.71 11710 2079.0
## + practice_sport:transport_means 2 8.80 11711 2079.0
## + gender:wkly_study_hours 2 1.29 11719 2079.4
## + gender:ethnic_group 4 76.47 11644 2079.6
## - test_prep:transport_means 1 139.37 11860 2080.4
## + practice_sport:wkly_study_hours 4 59.42 11661 2080.5
## + ethnic_group:transport_means 4 56.62 11664 2080.6
## + parent_marital_status:is_first_child 3 13.97 11706 2080.8
## + parent_marital_status:writing_score 3 12.30 11708 2080.9
## + parent_marital_status:reading_score 3 9.70 11710 2081.0
## - ethnic_group:is_first_child 4 287.75 12008 2081.8
## + ethnic_group:lunch_type 4 27.21 11693 2082.1
## - lunch_type:is_first_child 1 211.04 11931 2084.0
## + gender:parent_educ 5 16.22 11704 2084.7
## + ethnic_group:practice_sport 8 130.05 11590 2084.9
## - is_first_child:transport_means 1 229.99 11950 2084.9
## + parent_educ:wkly_study_hours 10 202.62 11518 2085.2
## + parent_educ:practice_sport 10 196.22 11524 2085.5
## + ethnic_group:parent_marital_status 11 204.85 11515 2087.1
## + ethnic_group:wkly_study_hours 8 81.31 11639 2087.4
## + parent_educ:parent_marital_status 15 234.21 11486 2093.6
##
## Step: AIC=2072.07
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:is_first_child + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 19.87 11752 2069.1
## - practice_sport:is_first_child 2 22.22 11754 2069.2
## - parent_marital_status:transport_means 3 64.19 11796 2069.3
## - lunch_type:parent_marital_status 2 31.98 11764 2069.7
## - ethnic_group:test_prep 4 116.24 11848 2069.9
## - parent_educ:reading_score 5 157.53 11889 2069.9
## - gender:lunch_type 1 0.13 11732 2070.1
## - lunch_type:transport_means 1 0.34 11732 2070.1
## - lunch_type:reading_score 1 0.43 11732 2070.1
## - parent_educ:test_prep 5 162.03 11894 2070.2
## - lunch_type:writing_score 1 1.97 11734 2070.2
## - gender:reading_score 1 2.32 11734 2070.2
## - test_prep:writing_score 1 2.41 11734 2070.2
## - gender:transport_means 1 2.59 11734 2070.2
## - transport_means:writing_score 1 2.60 11734 2070.2
## - test_prep:reading_score 1 3.55 11735 2070.2
## - gender:test_prep 1 3.99 11736 2070.3
## - is_first_child:writing_score 1 4.35 11736 2070.3
## - transport_means:reading_score 1 4.74 11737 2070.3
## - parent_educ:transport_means 5 165.33 11897 2070.3
## - test_prep:is_first_child 1 5.69 11738 2070.3
## - gender:is_first_child 1 5.89 11738 2070.4
## - test_prep:wkly_study_hours 2 46.97 11779 2070.4
## - lunch_type:test_prep 1 7.86 11740 2070.5
## - parent_marital_status:wkly_study_hours 6 209.27 11941 2070.5
## - parent_educ:writing_score 5 175.27 11907 2070.8
## - parent_educ:lunch_type 5 175.44 11907 2070.8
## - wkly_study_hours:writing_score 2 56.21 11788 2070.9
## - is_first_child:reading_score 1 19.30 11751 2071.0
## - writing_score:reading_score 1 21.23 11753 2071.1
## - lunch_type:wkly_study_hours 2 61.34 11793 2071.1
## - gender:parent_marital_status 3 106.51 11838 2071.4
## - gender:writing_score 1 31.50 11763 2071.7
## <none> 11732 2072.1
## - ethnic_group:reading_score 4 160.50 11892 2072.1
## - ethnic_group:writing_score 4 163.95 11896 2072.2
## - parent_marital_status:practice_sport 5 213.06 11945 2072.7
## - ethnic_group:parent_educ 20 839.27 12571 2072.8
## - practice_sport:writing_score 2 102.73 11835 2073.2
## - practice_sport:reading_score 2 103.40 11835 2073.2
## - is_first_child:wkly_study_hours 2 121.01 11853 2074.1
## - parent_educ:is_first_child 5 247.43 11979 2074.4
## - test_prep:parent_marital_status 3 176.10 11908 2074.9
## - lunch_type:practice_sport 2 145.50 11877 2075.3
## - wkly_study_hours:reading_score 2 147.77 11880 2075.4
## + gender:practice_sport 2 11.70 11720 2075.5
## + practice_sport:transport_means 2 10.50 11721 2075.5
## + test_prep:practice_sport 2 8.17 11724 2075.7
## + gender:wkly_study_hours 2 1.54 11730 2076.0
## + gender:ethnic_group 4 77.71 11654 2076.2
## + practice_sport:wkly_study_hours 4 66.16 11666 2076.7
## - test_prep:transport_means 1 139.27 11871 2077.0
## + ethnic_group:transport_means 4 59.82 11672 2077.1
## + parent_marital_status:is_first_child 3 15.04 11717 2077.3
## + parent_marital_status:writing_score 3 12.63 11719 2077.4
## + parent_marital_status:reading_score 3 11.30 11721 2077.5
## - ethnic_group:is_first_child 4 289.73 12022 2078.5
## + ethnic_group:lunch_type 4 26.52 11705 2078.7
## + gender:parent_educ 5 14.69 11717 2081.3
## + ethnic_group:practice_sport 8 131.24 11601 2081.4
## - is_first_child:transport_means 1 229.18 11961 2081.5
## - lunch_type:is_first_child 1 230.00 11962 2081.5
## + parent_educ:wkly_study_hours 10 203.94 11528 2081.7
## + parent_educ:practice_sport 10 199.48 11532 2081.9
## + ethnic_group:parent_marital_status 11 209.53 11522 2083.4
## + ethnic_group:wkly_study_hours 8 80.42 11652 2084.0
## + parent_educ:parent_marital_status 15 241.64 11490 2089.8
##
## Step: AIC=2069.06
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:is_first_child + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 3 63.35 11815 2066.2
## - practice_sport:is_first_child 2 23.88 11776 2066.3
## - lunch_type:parent_marital_status 2 29.57 11781 2066.6
## - parent_educ:reading_score 5 159.41 11911 2067.0
## - parent_educ:test_prep 5 159.51 11911 2067.0
## - parent_educ:transport_means 5 160.45 11912 2067.1
## - gender:lunch_type 1 0.13 11752 2067.1
## - lunch_type:transport_means 1 0.18 11752 2067.1
## - lunch_type:reading_score 1 0.93 11753 2067.1
## - gender:transport_means 1 2.17 11754 2067.2
## - test_prep:writing_score 1 2.78 11754 2067.2
## - lunch_type:writing_score 1 2.88 11755 2067.2
## - ethnic_group:test_prep 4 123.05 11875 2067.2
## - test_prep:wkly_study_hours 2 42.89 11795 2067.2
## - transport_means:writing_score 1 3.13 11755 2067.2
## - gender:reading_score 1 3.98 11756 2067.3
## - parent_marital_status:wkly_study_hours 6 205.06 11957 2067.3
## - gender:test_prep 1 4.12 11756 2067.3
## - test_prep:reading_score 1 4.18 11756 2067.3
## - transport_means:reading_score 1 4.25 11756 2067.3
## - is_first_child:writing_score 1 4.82 11757 2067.3
## - test_prep:is_first_child 1 5.44 11757 2067.3
## - lunch_type:test_prep 1 6.04 11758 2067.4
## - gender:is_first_child 1 8.23 11760 2067.5
## - lunch_type:wkly_study_hours 2 54.53 11806 2067.8
## - wkly_study_hours:writing_score 2 56.62 11808 2067.9
## - parent_educ:writing_score 5 179.81 11932 2068.0
## - is_first_child:reading_score 1 20.94 11773 2068.1
## - writing_score:reading_score 1 23.99 11776 2068.3
## - gender:parent_marital_status 3 110.86 11863 2068.6
## - parent_educ:lunch_type 5 192.25 11944 2068.6
## - ethnic_group:reading_score 4 154.12 11906 2068.8
## - gender:writing_score 1 35.92 11788 2068.9
## - ethnic_group:writing_score 4 159.49 11911 2069.0
## <none> 11752 2069.1
## - ethnic_group:parent_educ 20 829.83 12582 2069.3
## - parent_marital_status:practice_sport 5 206.09 11958 2069.3
## - practice_sport:reading_score 2 107.48 11859 2070.4
## - practice_sport:writing_score 2 109.03 11861 2070.5
## - is_first_child:wkly_study_hours 2 122.78 11874 2071.2
## - parent_educ:is_first_child 5 252.59 12004 2071.6
## - test_prep:parent_marital_status 3 173.51 11925 2071.7
## + transport_means:wkly_study_hours 2 19.87 11732 2072.1
## - lunch_type:practice_sport 2 146.03 11898 2072.3
## + gender:practice_sport 2 10.92 11741 2072.5
## + practice_sport:transport_means 2 10.15 11742 2072.6
## - wkly_study_hours:reading_score 2 151.33 11903 2072.6
## + test_prep:practice_sport 2 7.07 11745 2072.7
## + gender:wkly_study_hours 2 1.96 11750 2073.0
## + gender:ethnic_group 4 76.90 11675 2073.2
## + ethnic_group:transport_means 4 65.98 11686 2073.7
## + practice_sport:wkly_study_hours 4 58.35 11693 2074.1
## - test_prep:transport_means 1 143.84 11896 2074.2
## + parent_marital_status:is_first_child 3 15.32 11736 2074.3
## + parent_marital_status:writing_score 3 12.39 11739 2074.4
## + parent_marital_status:reading_score 3 10.23 11742 2074.6
## + ethnic_group:lunch_type 4 27.80 11724 2075.7
## - ethnic_group:is_first_child 4 298.14 12050 2075.8
## - lunch_type:is_first_child 1 220.68 11972 2078.0
## + gender:parent_educ 5 15.88 11736 2078.3
## - is_first_child:transport_means 1 230.09 11982 2078.5
## + parent_educ:practice_sport 10 202.79 11549 2078.8
## + ethnic_group:practice_sport 8 117.05 11635 2079.2
## + parent_educ:wkly_study_hours 10 190.94 11561 2079.4
## + ethnic_group:parent_marital_status 11 211.77 11540 2080.3
## + ethnic_group:wkly_study_hours 8 88.57 11663 2080.6
## + parent_educ:parent_marital_status 15 247.77 11504 2086.5
##
## Step: AIC=2066.24
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:is_first_child + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## parent_marital_status:wkly_study_hours + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:wkly_study_hours 6 178.00 11993 2063.1
## - practice_sport:is_first_child 2 20.82 11836 2063.3
## - lunch_type:parent_marital_status 2 27.79 11843 2063.6
## - test_prep:wkly_study_hours 2 34.51 11850 2064.0
## - parent_educ:test_prep 5 158.17 11973 2064.1
## - parent_educ:reading_score 5 159.13 11974 2064.1
## - gender:lunch_type 1 0.01 11815 2064.2
## - lunch_type:reading_score 1 0.17 11815 2064.2
## - lunch_type:transport_means 1 0.47 11816 2064.3
## - lunch_type:writing_score 1 1.00 11816 2064.3
## - gender:transport_means 1 1.70 11817 2064.3
## - transport_means:reading_score 1 2.65 11818 2064.4
## - test_prep:writing_score 1 2.69 11818 2064.4
## - is_first_child:writing_score 1 3.48 11819 2064.4
## - gender:reading_score 1 3.50 11819 2064.4
## - gender:test_prep 1 4.05 11819 2064.4
## - transport_means:writing_score 1 4.48 11820 2064.5
## - test_prep:reading_score 1 4.73 11820 2064.5
## - parent_educ:transport_means 5 167.77 11983 2064.6
## - gender:is_first_child 1 6.60 11822 2064.6
## - lunch_type:test_prep 1 6.84 11822 2064.6
## - test_prep:is_first_child 1 7.35 11822 2064.6
## - ethnic_group:test_prep 4 130.46 11946 2064.7
## - gender:parent_marital_status 3 95.61 11911 2065.0
## - wkly_study_hours:writing_score 2 58.54 11874 2065.2
## - parent_educ:writing_score 5 179.92 11995 2065.2
## - is_first_child:reading_score 1 19.04 11834 2065.2
## - writing_score:reading_score 1 20.67 11836 2065.3
## - lunch_type:wkly_study_hours 2 61.21 11876 2065.3
## - parent_educ:lunch_type 5 192.04 12007 2065.8
## - gender:writing_score 1 37.56 11853 2066.1
## - ethnic_group:parent_educ 20 826.96 12642 2066.2
## <none> 11815 2066.2
## - ethnic_group:reading_score 4 165.36 11980 2066.4
## - ethnic_group:writing_score 4 165.87 11981 2066.5
## - test_prep:parent_marital_status 3 147.80 11963 2067.6
## - practice_sport:reading_score 2 108.84 11924 2067.7
## - practice_sport:writing_score 2 112.54 11928 2067.8
## - is_first_child:wkly_study_hours 2 117.82 11933 2068.1
## - parent_marital_status:practice_sport 5 249.71 12065 2068.6
## + parent_marital_status:transport_means 3 63.35 11752 2069.1
## + transport_means:wkly_study_hours 2 19.02 11796 2069.3
## + gender:practice_sport 2 17.46 11798 2069.4
## - lunch_type:practice_sport 2 147.90 11963 2069.6
## + practice_sport:transport_means 2 12.06 11803 2069.6
## - parent_educ:is_first_child 5 271.87 12087 2069.7
## - wkly_study_hours:reading_score 2 154.57 11970 2069.9
## + test_prep:practice_sport 2 4.97 11810 2070.0
## + gender:ethnic_group 4 83.31 11732 2070.1
## + gender:wkly_study_hours 2 1.81 11813 2070.2
## + parent_marital_status:is_first_child 3 26.64 11788 2070.9
## - test_prep:transport_means 1 141.25 11956 2071.2
## + ethnic_group:transport_means 4 56.78 11758 2071.4
## + parent_marital_status:writing_score 3 8.42 11807 2071.8
## + parent_marital_status:reading_score 3 6.98 11808 2071.9
## + practice_sport:wkly_study_hours 4 40.16 11775 2072.2
## + ethnic_group:lunch_type 4 30.28 11785 2072.7
## - ethnic_group:is_first_child 4 305.40 12120 2073.3
## - is_first_child:transport_means 1 221.80 12037 2075.2
## - lunch_type:is_first_child 1 224.54 12040 2075.3
## + gender:parent_educ 5 13.02 11802 2075.6
## + parent_educ:practice_sport 10 199.93 11615 2076.2
## + ethnic_group:practice_sport 8 111.76 11703 2076.6
## + ethnic_group:wkly_study_hours 8 103.36 11712 2077.1
## + parent_educ:wkly_study_hours 10 168.22 11647 2077.8
## + ethnic_group:parent_marital_status 11 196.07 11619 2078.4
## + parent_educ:parent_marital_status 15 236.82 11578 2084.3
##
## Step: AIC=2063.06
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:parent_marital_status +
## gender:is_first_child + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:parent_educ + ethnic_group:test_prep +
## ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 47.01 12040 2059.4
## - practice_sport:is_first_child 2 14.75 12008 2059.8
## - ethnic_group:parent_educ 20 777.17 12770 2060.1
## - lunch_type:parent_marital_status 2 23.19 12016 2060.2
## - parent_educ:reading_score 5 150.98 12144 2060.4
## - test_prep:wkly_study_hours 2 31.89 12025 2060.6
## - lunch_type:transport_means 1 0.07 11993 2061.1
## - lunch_type:reading_score 1 0.68 11994 2061.1
## - transport_means:reading_score 1 0.89 11994 2061.1
## - gender:transport_means 1 1.00 11994 2061.1
## - gender:test_prep 1 1.48 11995 2061.1
## - lunch_type:test_prep 1 1.53 11995 2061.1
## - gender:reading_score 1 1.63 11995 2061.1
## - gender:lunch_type 1 1.73 11995 2061.1
## - lunch_type:writing_score 1 2.14 11995 2061.2
## - gender:is_first_child 1 2.37 11996 2061.2
## - test_prep:writing_score 1 2.77 11996 2061.2
## - is_first_child:writing_score 1 3.88 11997 2061.2
## - test_prep:reading_score 1 4.46 11998 2061.3
## - parent_educ:lunch_type 5 168.57 12162 2061.3
## - ethnic_group:test_prep 4 127.78 12121 2061.3
## - parent_educ:test_prep 5 168.99 12162 2061.3
## - test_prep:is_first_child 1 5.32 11998 2061.3
## - parent_educ:writing_score 5 169.54 12163 2061.3
## - transport_means:writing_score 1 7.71 12001 2061.4
## - wkly_study_hours:writing_score 2 49.08 12042 2061.5
## - lunch_type:wkly_study_hours 2 54.20 12047 2061.7
## - is_first_child:reading_score 1 21.65 12015 2062.1
## - writing_score:reading_score 1 23.68 12017 2062.2
## - parent_educ:transport_means 5 191.53 12185 2062.4
## - gender:writing_score 1 31.63 12025 2062.6
## <none> 11993 2063.1
## - test_prep:parent_marital_status 3 152.72 12146 2064.5
## - practice_sport:reading_score 2 118.66 12112 2064.9
## - practice_sport:writing_score 2 126.77 12120 2065.3
## - ethnic_group:reading_score 4 211.20 12204 2065.4
## - wkly_study_hours:reading_score 2 131.56 12125 2065.5
## - ethnic_group:writing_score 4 215.37 12208 2065.6
## - lunch_type:practice_sport 2 133.40 12126 2065.6
## + gender:practice_sport 2 24.04 11969 2065.9
## - parent_marital_status:practice_sport 5 269.16 12262 2066.2
## + parent_marital_status:wkly_study_hours 6 178.00 11815 2066.2
## + transport_means:wkly_study_hours 2 15.92 11977 2066.3
## - parent_educ:is_first_child 5 272.33 12265 2066.3
## + practice_sport:transport_means 2 10.68 11982 2066.5
## + gender:wkly_study_hours 2 9.46 11984 2066.6
## + test_prep:practice_sport 2 5.03 11988 2066.8
## + gender:ethnic_group 4 83.41 11910 2066.9
## - is_first_child:wkly_study_hours 2 163.08 12156 2067.0
## + parent_marital_status:transport_means 3 36.28 11957 2067.3
## + parent_marital_status:writing_score 3 23.50 11970 2067.9
## + parent_marital_status:is_first_child 3 20.56 11972 2068.1
## - test_prep:transport_means 1 146.49 12140 2068.2
## + parent_marital_status:reading_score 3 16.62 11976 2068.2
## + ethnic_group:transport_means 4 45.38 11948 2068.8
## + practice_sport:wkly_study_hours 4 31.67 11961 2069.5
## - ethnic_group:is_first_child 4 304.17 12297 2069.8
## + ethnic_group:lunch_type 4 22.84 11970 2069.9
## - lunch_type:is_first_child 1 210.47 12204 2071.3
## + parent_educ:practice_sport 10 218.59 11774 2072.2
## + gender:parent_educ 5 8.50 11985 2072.6
## + ethnic_group:parent_marital_status 11 249.36 11744 2072.7
## + ethnic_group:practice_sport 8 114.27 11879 2073.4
## + parent_educ:wkly_study_hours 10 179.28 11814 2074.2
## + ethnic_group:wkly_study_hours 8 95.91 11897 2074.3
## - is_first_child:transport_means 1 285.88 12279 2075.0
## + parent_educ:parent_marital_status 15 243.78 11749 2080.9
##
## Step: AIC=2059.37
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:parent_educ + ethnic_group:test_prep + ethnic_group:is_first_child +
## ethnic_group:writing_score + ethnic_group:reading_score +
## parent_educ:lunch_type + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:reading_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:parent_educ 20 761.88 12802 2055.6
## - practice_sport:is_first_child 2 19.20 12059 2056.3
## - parent_educ:reading_score 5 150.49 12191 2056.7
## - lunch_type:parent_marital_status 2 28.00 12068 2056.7
## - ethnic_group:test_prep 4 116.40 12156 2057.0
## - test_prep:wkly_study_hours 2 34.93 12075 2057.1
## - parent_educ:test_prep 5 158.45 12199 2057.1
## - parent_educ:lunch_type 5 162.89 12203 2057.3
## - lunch_type:transport_means 1 0.03 12040 2057.4
## - transport_means:reading_score 1 0.13 12040 2057.4
## - gender:reading_score 1 0.70 12041 2057.4
## - lunch_type:reading_score 1 0.76 12041 2057.4
## - gender:transport_means 1 0.79 12041 2057.4
## - gender:lunch_type 1 1.07 12041 2057.4
## - gender:test_prep 1 1.34 12041 2057.4
## - lunch_type:writing_score 1 1.96 12042 2057.5
## - gender:is_first_child 1 2.71 12043 2057.5
## - lunch_type:test_prep 1 2.80 12043 2057.5
## - test_prep:writing_score 1 4.04 12044 2057.6
## - is_first_child:writing_score 1 4.09 12044 2057.6
## - parent_educ:writing_score 5 169.04 12209 2057.6
## - test_prep:is_first_child 1 4.88 12045 2057.6
## - test_prep:reading_score 1 7.16 12047 2057.7
## - wkly_study_hours:writing_score 2 49.59 12090 2057.8
## - transport_means:writing_score 1 11.03 12051 2057.9
## - lunch_type:wkly_study_hours 2 57.38 12098 2058.2
## - writing_score:reading_score 1 21.16 12061 2058.4
## - is_first_child:reading_score 1 22.05 12062 2058.4
## - gender:writing_score 1 26.64 12067 2058.7
## - parent_educ:transport_means 5 199.12 12239 2059.0
## <none> 12040 2059.4
## - practice_sport:reading_score 2 115.83 12156 2061.0
## - test_prep:parent_marital_status 3 160.84 12201 2061.2
## - practice_sport:writing_score 2 124.74 12165 2061.4
## - wkly_study_hours:reading_score 2 128.76 12169 2061.6
## - lunch_type:practice_sport 2 129.02 12169 2061.7
## - ethnic_group:reading_score 4 216.36 12256 2061.9
## - parent_marital_status:practice_sport 5 258.54 12299 2061.9
## - ethnic_group:writing_score 4 218.56 12259 2062.0
## + gender:practice_sport 2 23.24 12017 2062.2
## + transport_means:wkly_study_hours 2 20.32 12020 2062.4
## - parent_educ:is_first_child 5 275.56 12316 2062.7
## + gender:wkly_study_hours 2 11.79 12028 2062.8
## + practice_sport:transport_means 2 8.42 12032 2062.9
## + gender:ethnic_group 4 87.91 11952 2063.0
## + test_prep:practice_sport 2 6.47 12034 2063.1
## + gender:parent_marital_status 3 47.01 11993 2063.1
## + parent_marital_status:is_first_child 3 43.60 11996 2063.2
## + parent_marital_status:transport_means 3 37.95 12002 2063.5
## - is_first_child:wkly_study_hours 2 170.54 12211 2063.7
## - test_prep:transport_means 1 149.93 12190 2064.7
## + parent_marital_status:writing_score 3 12.28 12028 2064.8
## + parent_marital_status:reading_score 3 9.60 12030 2064.9
## + parent_marital_status:wkly_study_hours 6 129.39 11911 2065.0
## + ethnic_group:transport_means 4 47.82 11992 2065.0
## + practice_sport:wkly_study_hours 4 38.07 12002 2065.5
## - ethnic_group:is_first_child 4 303.95 12344 2066.1
## + ethnic_group:lunch_type 4 23.44 12017 2066.2
## + ethnic_group:parent_marital_status 11 291.26 11749 2066.9
## - lunch_type:is_first_child 1 214.71 12255 2067.8
## + gender:parent_educ 5 6.46 12034 2069.1
## + parent_educ:practice_sport 10 202.74 11837 2069.3
## + ethnic_group:practice_sport 8 118.40 11922 2069.5
## + parent_educ:wkly_study_hours 10 177.47 11863 2070.6
## + ethnic_group:wkly_study_hours 8 84.98 11955 2071.2
## - is_first_child:transport_means 1 296.04 12336 2071.7
## + parent_educ:parent_marital_status 15 250.25 11790 2077.0
##
## Step: AIC=2055.57
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:reading_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:reading_score 5 99.29 12901 2050.1
## - parent_educ:writing_score 5 121.86 12924 2051.2
## - parent_educ:lunch_type 5 154.92 12957 2052.7
## - practice_sport:is_first_child 2 40.83 12843 2053.4
## - lunch_type:parent_marital_status 2 41.58 12844 2053.5
## - lunch_type:test_prep 1 0.19 12802 2053.6
## - gender:is_first_child 1 0.28 12802 2053.6
## - gender:transport_means 1 0.50 12802 2053.6
## - lunch_type:transport_means 1 0.56 12802 2053.6
## - gender:reading_score 1 0.64 12803 2053.6
## - gender:lunch_type 1 0.75 12803 2053.6
## - is_first_child:reading_score 1 0.80 12803 2053.6
## - transport_means:reading_score 1 0.85 12803 2053.6
## - test_prep:writing_score 1 3.12 12805 2053.7
## - is_first_child:writing_score 1 3.26 12805 2053.7
## - test_prep:is_first_child 1 3.46 12805 2053.7
## - test_prep:wkly_study_hours 2 48.35 12850 2053.8
## - lunch_type:reading_score 1 5.45 12807 2053.8
## - lunch_type:writing_score 1 6.37 12808 2053.9
## - test_prep:reading_score 1 7.70 12810 2053.9
## - wkly_study_hours:writing_score 2 51.61 12854 2053.9
## - transport_means:writing_score 1 9.25 12811 2054.0
## - gender:test_prep 1 10.75 12813 2054.1
## - writing_score:reading_score 1 11.51 12814 2054.1
## - parent_educ:test_prep 5 193.00 12995 2054.4
## - gender:writing_score 1 24.39 12826 2054.7
## - ethnic_group:test_prep 4 157.08 12959 2054.8
## - ethnic_group:reading_score 4 158.29 12960 2054.8
## - ethnic_group:writing_score 4 163.74 12966 2055.1
## - lunch_type:wkly_study_hours 2 80.06 12882 2055.2
## <none> 12802 2055.6
## - lunch_type:practice_sport 2 93.02 12895 2055.8
## - parent_educ:transport_means 5 227.14 13029 2055.9
## - test_prep:parent_marital_status 3 153.38 12955 2056.6
## - parent_marital_status:practice_sport 5 245.91 13048 2056.8
## + practice_sport:transport_means 2 45.02 12757 2057.5
## + gender:ethnic_group 4 126.01 12676 2057.7
## - wkly_study_hours:reading_score 2 138.39 12940 2057.9
## - parent_educ:is_first_child 5 277.92 13080 2058.2
## + gender:practice_sport 2 22.49 12780 2058.5
## + gender:wkly_study_hours 2 20.55 12781 2058.6
## - practice_sport:reading_score 2 158.02 12960 2058.8
## - practice_sport:writing_score 2 163.45 12965 2059.1
## + test_prep:practice_sport 2 11.00 12791 2059.1
## + transport_means:wkly_study_hours 2 10.37 12792 2059.1
## + ethnic_group:parent_educ 20 761.88 12040 2059.4
## - test_prep:transport_means 1 133.98 12936 2059.7
## + parent_marital_status:transport_means 3 38.78 12763 2059.8
## - ethnic_group:is_first_child 4 272.11 13074 2060.0
## + gender:parent_marital_status 3 31.72 12770 2060.1
## + parent_marital_status:is_first_child 3 28.07 12774 2060.3
## - is_first_child:wkly_study_hours 2 201.32 13003 2060.8
## + ethnic_group:lunch_type 4 57.78 12744 2060.9
## - lunch_type:is_first_child 1 162.17 12964 2061.0
## + ethnic_group:transport_means 4 50.62 12751 2061.2
## + parent_marital_status:writing_score 3 4.10 12798 2061.4
## + parent_marital_status:reading_score 3 3.55 12798 2061.4
## + practice_sport:wkly_study_hours 4 10.27 12792 2063.1
## + ethnic_group:parent_marital_status 11 308.30 12494 2063.2
## + parent_marital_status:wkly_study_hours 6 91.87 12710 2063.3
## + ethnic_group:practice_sport 8 171.92 12630 2063.6
## + gender:parent_educ 5 26.78 12775 2064.3
## + parent_educ:practice_sport 10 194.28 12608 2066.5
## - is_first_child:transport_means 1 301.30 13103 2067.3
## + ethnic_group:wkly_study_hours 8 80.42 12722 2067.8
## + parent_educ:wkly_study_hours 10 161.83 12640 2068.1
## + parent_educ:parent_marital_status 15 307.27 12495 2071.2
##
## Step: AIC=2050.13
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:writing_score 5 132.93 13034 2046.2
## - parent_educ:lunch_type 5 144.54 13046 2046.7
## - lunch_type:parent_marital_status 2 43.17 12944 2048.1
## - gender:reading_score 1 0.02 12901 2048.1
## - gender:is_first_child 1 0.02 12901 2048.1
## - lunch_type:test_prep 1 0.06 12901 2048.1
## - transport_means:reading_score 1 0.25 12902 2048.1
## - gender:lunch_type 1 0.30 12902 2048.1
## - is_first_child:writing_score 1 1.35 12903 2048.2
## - lunch_type:transport_means 1 1.48 12903 2048.2
## - gender:transport_means 1 1.74 12903 2048.2
## - is_first_child:reading_score 1 2.51 12904 2048.2
## - parent_educ:test_prep 5 178.73 13080 2048.2
## - wkly_study_hours:writing_score 2 47.43 12949 2048.3
## - practice_sport:is_first_child 2 47.87 12949 2048.3
## - test_prep:writing_score 1 4.52 12906 2048.3
## - lunch_type:writing_score 1 5.11 12906 2048.4
## - lunch_type:reading_score 1 5.23 12906 2048.4
## - test_prep:is_first_child 1 5.82 12907 2048.4
## - gender:test_prep 1 9.38 12911 2048.6
## - test_prep:wkly_study_hours 2 54.22 12956 2048.6
## - writing_score:reading_score 1 10.62 12912 2048.6
## - test_prep:reading_score 1 11.24 12912 2048.6
## - transport_means:writing_score 1 12.87 12914 2048.7
## - ethnic_group:reading_score 4 147.16 13048 2048.8
## - ethnic_group:test_prep 4 147.50 13049 2048.8
## - ethnic_group:writing_score 4 149.16 13050 2048.9
## - gender:writing_score 1 18.32 12920 2049.0
## <none> 12901 2050.1
## - lunch_type:wkly_study_hours 2 88.07 12989 2050.1
## - lunch_type:practice_sport 2 88.33 12990 2050.2
## - parent_marital_status:practice_sport 5 231.06 13132 2050.6
## - parent_educ:transport_means 5 232.96 13134 2050.7
## - test_prep:parent_marital_status 3 153.48 13055 2051.1
## - wkly_study_hours:reading_score 2 128.65 13030 2052.0
## + practice_sport:transport_means 2 36.08 12865 2052.5
## + gender:wkly_study_hours 2 22.07 12879 2053.1
## + gender:ethnic_group 4 107.56 12794 2053.2
## + gender:practice_sport 2 18.23 12883 2053.3
## + transport_means:wkly_study_hours 2 9.21 12892 2053.7
## + test_prep:practice_sport 2 8.02 12893 2053.8
## - practice_sport:writing_score 2 175.39 13077 2054.1
## - practice_sport:reading_score 2 177.29 13079 2054.2
## - ethnic_group:is_first_child 4 268.16 13169 2054.3
## + parent_marital_status:transport_means 3 36.54 12865 2054.4
## - test_prep:transport_means 1 140.19 13042 2054.5
## + gender:parent_marital_status 3 32.21 12869 2054.7
## + parent_marital_status:is_first_child 3 25.26 12876 2055.0
## - parent_educ:is_first_child 5 338.63 13240 2055.4
## + ethnic_group:lunch_type 4 57.08 12844 2055.5
## - lunch_type:is_first_child 1 163.21 13064 2055.5
## + parent_educ:reading_score 5 99.29 12802 2055.6
## - is_first_child:wkly_study_hours 2 209.25 13110 2055.6
## + parent_marital_status:reading_score 3 5.31 12896 2055.9
## + parent_marital_status:writing_score 3 4.53 12897 2055.9
## + ethnic_group:transport_means 4 45.84 12855 2056.0
## + ethnic_group:parent_educ 20 710.68 12191 2056.7
## + parent_marital_status:wkly_study_hours 6 94.01 12807 2057.8
## + practice_sport:wkly_study_hours 4 4.76 12896 2057.9
## + ethnic_group:parent_marital_status 11 291.03 12610 2058.7
## + ethnic_group:practice_sport 8 159.66 12742 2058.8
## + gender:parent_educ 5 17.54 12884 2059.3
## + parent_educ:practice_sport 10 198.47 12703 2061.0
## - is_first_child:transport_means 1 305.26 13206 2061.9
## + parent_educ:wkly_study_hours 10 161.81 12740 2062.7
## + ethnic_group:wkly_study_hours 8 71.42 12830 2062.8
## + parent_educ:parent_marital_status 15 291.89 12609 2066.6
##
## Step: AIC=2046.17
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:lunch_type + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 149.37 13184 2042.9
## - lunch_type:parent_marital_status 2 37.45 13072 2043.9
## - ethnic_group:reading_score 4 129.34 13164 2044.0
## - parent_educ:test_prep 5 174.12 13208 2044.0
## - ethnic_group:writing_score 4 132.21 13166 2044.1
## - lunch_type:test_prep 1 0.00 13034 2044.2
## - gender:reading_score 1 0.11 13034 2044.2
## - gender:is_first_child 1 0.12 13034 2044.2
## - gender:lunch_type 1 0.28 13034 2044.2
## - lunch_type:transport_means 1 0.59 13035 2044.2
## - practice_sport:is_first_child 2 45.12 13079 2044.2
## - is_first_child:writing_score 1 1.23 13035 2044.2
## - test_prep:writing_score 1 1.25 13036 2044.2
## - is_first_child:reading_score 1 1.37 13036 2044.2
## - gender:transport_means 1 1.61 13036 2044.2
## - transport_means:reading_score 1 1.99 13036 2044.3
## - lunch_type:reading_score 1 2.53 13037 2044.3
## - lunch_type:writing_score 1 2.83 13037 2044.3
## - test_prep:reading_score 1 4.94 13039 2044.4
## - test_prep:wkly_study_hours 2 50.51 13085 2044.5
## - transport_means:writing_score 1 6.37 13041 2044.5
## - test_prep:is_first_child 1 8.15 13042 2044.5
## - gender:test_prep 1 8.99 13043 2044.6
## - wkly_study_hours:writing_score 2 57.10 13091 2044.8
## - gender:writing_score 1 13.28 13048 2044.8
## - ethnic_group:test_prep 4 153.20 13187 2045.1
## - writing_score:reading_score 1 32.85 13067 2045.7
## - lunch_type:wkly_study_hours 2 86.60 13121 2046.1
## <none> 13034 2046.2
## - parent_educ:transport_means 5 227.22 13261 2046.4
## - lunch_type:practice_sport 2 98.79 13133 2046.6
## - parent_marital_status:practice_sport 5 233.78 13268 2046.7
## - test_prep:parent_marital_status 3 165.30 13200 2047.6
## + practice_sport:transport_means 2 44.11 12990 2048.2
## - wkly_study_hours:reading_score 2 148.86 13183 2048.9
## + gender:wkly_study_hours 2 24.32 13010 2049.1
## + gender:ethnic_group 4 107.46 12927 2049.3
## + gender:practice_sport 2 13.88 13020 2049.5
## + transport_means:wkly_study_hours 2 11.98 13022 2049.6
## + test_prep:practice_sport 2 7.52 13027 2049.8
## - test_prep:transport_means 1 126.19 13160 2049.9
## + parent_educ:writing_score 5 132.93 12901 2050.1
## + parent_marital_status:transport_means 3 41.71 12992 2050.3
## - ethnic_group:is_first_child 4 275.08 13309 2050.5
## + gender:parent_marital_status 3 34.76 12999 2050.6
## - practice_sport:reading_score 2 194.03 13228 2050.9
## - practice_sport:writing_score 2 194.79 13229 2050.9
## + parent_marital_status:is_first_child 3 24.10 13010 2051.1
## + parent_educ:reading_score 5 110.35 12924 2051.2
## + ethnic_group:lunch_type 4 62.92 12971 2051.3
## - parent_educ:is_first_child 5 350.50 13385 2051.8
## - is_first_child:wkly_study_hours 2 217.55 13252 2051.9
## + parent_marital_status:writing_score 3 3.61 13031 2052.0
## + parent_marital_status:reading_score 3 2.81 13031 2052.1
## + ethnic_group:transport_means 4 42.26 12992 2052.3
## + ethnic_group:parent_educ 20 705.65 12328 2053.3
## - lunch_type:is_first_child 1 215.45 13250 2053.8
## + gender:parent_educ 5 48.26 12986 2054.0
## + practice_sport:wkly_study_hours 4 2.30 13032 2054.1
## + parent_marital_status:wkly_study_hours 6 82.07 12952 2054.4
## + ethnic_group:practice_sport 8 167.80 12866 2054.5
## + ethnic_group:parent_marital_status 11 281.37 12753 2055.3
## - is_first_child:transport_means 1 299.22 13333 2057.6
## + parent_educ:practice_sport 10 178.84 12855 2058.0
## + ethnic_group:wkly_study_hours 8 76.15 12958 2058.7
## + parent_educ:wkly_study_hours 10 152.18 12882 2059.2
## + parent_educ:parent_marital_status 15 332.73 12702 2060.9
##
## Step: AIC=2042.9
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## ethnic_group:reading_score + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:reading_score 4 110.19 13294 2039.8
## - ethnic_group:writing_score 4 117.20 13301 2040.1
## - practice_sport:is_first_child 2 41.58 13225 2040.8
## - lunch_type:parent_marital_status 2 43.90 13228 2040.9
## - gender:is_first_child 1 0.00 13184 2040.9
## - is_first_child:reading_score 1 0.09 13184 2040.9
## - transport_means:reading_score 1 0.14 13184 2040.9
## - lunch_type:test_prep 1 0.16 13184 2040.9
## - gender:reading_score 1 0.16 13184 2040.9
## - gender:lunch_type 1 0.81 13184 2040.9
## - lunch_type:writing_score 1 0.92 13184 2040.9
## - lunch_type:reading_score 1 1.36 13185 2041.0
## - test_prep:writing_score 1 2.01 13186 2041.0
## - lunch_type:transport_means 1 3.17 13187 2041.0
## - test_prep:wkly_study_hours 2 48.09 13232 2041.0
## - is_first_child:writing_score 1 3.49 13187 2041.0
## - parent_educ:test_prep 5 183.90 13368 2041.1
## - gender:test_prep 1 5.19 13189 2041.1
## - test_prep:reading_score 1 5.50 13189 2041.1
## - gender:transport_means 1 5.73 13189 2041.2
## - wkly_study_hours:writing_score 2 51.56 13235 2041.2
## - test_prep:is_first_child 1 6.82 13190 2041.2
## - transport_means:writing_score 1 11.36 13195 2041.4
## - gender:writing_score 1 18.03 13202 2041.7
## - writing_score:reading_score 1 32.07 13216 2042.3
## - lunch_type:practice_sport 2 84.09 13268 2042.7
## - ethnic_group:test_prep 4 174.68 13358 2042.7
## <none> 13184 2042.9
## - parent_educ:transport_means 5 229.86 13413 2043.1
## - lunch_type:wkly_study_hours 2 97.27 13281 2043.2
## - test_prep:parent_marital_status 3 162.56 13346 2044.1
## - parent_marital_status:practice_sport 5 259.71 13443 2044.4
## + practice_sport:transport_means 2 46.36 13137 2044.8
## - wkly_study_hours:reading_score 2 135.42 13319 2044.9
## + transport_means:wkly_study_hours 2 20.65 13163 2046.0
## + gender:wkly_study_hours 2 17.75 13166 2046.1
## + gender:ethnic_group 4 106.45 13077 2046.1
## + parent_educ:lunch_type 5 149.37 13034 2046.2
## + gender:practice_sport 2 12.74 13171 2046.3
## + test_prep:practice_sport 2 12.20 13171 2046.3
## + parent_educ:writing_score 5 137.76 13046 2046.7
## + parent_educ:reading_score 5 134.53 13049 2046.8
## - parent_educ:is_first_child 5 316.22 13500 2046.9
## + parent_marital_status:transport_means 3 41.45 13142 2047.0
## + gender:parent_marital_status 3 31.51 13152 2047.5
## - test_prep:transport_means 1 149.86 13333 2047.6
## - ethnic_group:is_first_child 4 286.27 13470 2047.6
## - practice_sport:reading_score 2 197.75 13381 2047.7
## + ethnic_group:lunch_type 4 68.75 13115 2047.8
## - practice_sport:writing_score 2 202.65 13386 2047.9
## + parent_marital_status:is_first_child 3 18.93 13165 2048.1
## + parent_marital_status:writing_score 3 7.74 13176 2048.6
## + parent_marital_status:reading_score 3 7.34 13176 2048.6
## + ethnic_group:transport_means 4 49.95 13134 2048.7
## - is_first_child:wkly_study_hours 2 236.87 13420 2049.4
## - lunch_type:is_first_child 1 202.51 13386 2049.9
## + practice_sport:wkly_study_hours 4 2.96 13181 2050.8
## + gender:parent_educ 5 47.07 13136 2050.8
## + ethnic_group:practice_sport 8 175.74 13008 2051.0
## + ethnic_group:parent_educ 20 691.00 12493 2051.1
## + parent_marital_status:wkly_study_hours 6 62.37 13121 2052.1
## + ethnic_group:parent_marital_status 11 261.69 12922 2053.1
## + parent_educ:practice_sport 10 183.88 13000 2054.6
## - is_first_child:transport_means 1 313.26 13497 2054.8
## + ethnic_group:wkly_study_hours 8 81.47 13102 2055.2
## + parent_educ:wkly_study_hours 10 131.72 13052 2057.0
## + parent_educ:parent_marital_status 15 311.73 12872 2058.8
##
## Step: AIC=2039.81
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:writing_score 4 35.77 13330 2033.4
## - practice_sport:is_first_child 2 35.34 13329 2037.4
## - lunch_type:test_prep 1 0.00 13294 2037.8
## - gender:is_first_child 1 0.10 13294 2037.8
## - transport_means:reading_score 1 0.25 13294 2037.8
## - lunch_type:writing_score 1 0.26 13294 2037.8
## - lunch_type:reading_score 1 0.57 13294 2037.8
## - test_prep:writing_score 1 1.03 13295 2037.8
## - gender:lunch_type 1 1.27 13295 2037.9
## - is_first_child:reading_score 1 2.22 13296 2037.9
## - lunch_type:parent_marital_status 2 47.44 13341 2037.9
## - test_prep:reading_score 1 2.81 13297 2037.9
## - gender:transport_means 1 3.10 13297 2038.0
## - lunch_type:transport_means 1 3.27 13297 2038.0
## - test_prep:is_first_child 1 4.05 13298 2038.0
## - test_prep:wkly_study_hours 2 50.60 13344 2038.0
## - parent_educ:test_prep 5 187.46 13481 2038.1
## - gender:reading_score 1 8.85 13303 2038.2
## - gender:test_prep 1 9.34 13303 2038.2
## - transport_means:writing_score 1 10.35 13304 2038.3
## - is_first_child:writing_score 1 12.70 13306 2038.4
## - wkly_study_hours:writing_score 2 60.65 13354 2038.5
## - lunch_type:practice_sport 2 74.40 13368 2039.1
## - lunch_type:wkly_study_hours 2 78.66 13372 2039.3
## - writing_score:reading_score 1 38.42 13332 2039.5
## - gender:writing_score 1 43.10 13337 2039.7
## <none> 13294 2039.8
## - ethnic_group:test_prep 4 194.01 13488 2040.4
## - parent_educ:transport_means 5 245.55 13539 2040.6
## - test_prep:parent_marital_status 3 163.85 13458 2041.0
## - parent_marital_status:practice_sport 5 257.66 13551 2041.1
## + practice_sport:transport_means 2 46.29 13248 2041.8
## - wkly_study_hours:reading_score 2 149.05 13443 2042.4
## + ethnic_group:reading_score 4 110.19 13184 2042.9
## + gender:wkly_study_hours 2 17.62 13276 2043.0
## + transport_means:wkly_study_hours 2 13.21 13281 2043.2
## + gender:practice_sport 2 10.93 13283 2043.3
## - parent_educ:is_first_child 5 311.51 13605 2043.5
## + test_prep:practice_sport 2 6.99 13287 2043.5
## + parent_marital_status:transport_means 3 50.67 13243 2043.5
## - test_prep:transport_means 1 130.38 13424 2043.6
## + parent_educ:lunch_type 5 130.22 13164 2044.0
## + gender:ethnic_group 4 83.01 13211 2044.1
## + parent_educ:writing_score 5 126.11 13168 2044.2
## + gender:parent_marital_status 3 33.43 13260 2044.3
## + parent_educ:reading_score 5 119.35 13174 2044.5
## + ethnic_group:lunch_type 4 74.27 13220 2044.5
## + parent_marital_status:is_first_child 3 19.54 13274 2044.9
## + parent_marital_status:writing_score 3 14.08 13280 2045.2
## - is_first_child:wkly_study_hours 2 214.25 13508 2045.2
## - ethnic_group:is_first_child 4 307.90 13602 2045.3
## + parent_marital_status:reading_score 3 10.29 13284 2045.3
## + ethnic_group:transport_means 4 50.91 13243 2045.5
## - practice_sport:writing_score 2 222.36 13516 2045.6
## - practice_sport:reading_score 2 222.71 13516 2045.6
## - lunch_type:is_first_child 1 210.80 13505 2047.1
## + gender:parent_educ 5 49.54 13244 2047.6
## + practice_sport:wkly_study_hours 4 1.97 13292 2047.7
## + parent_marital_status:wkly_study_hours 6 85.61 13208 2048.0
## + ethnic_group:practice_sport 8 148.00 13146 2049.2
## + ethnic_group:parent_educ 20 651.69 12642 2050.2
## + ethnic_group:parent_marital_status 11 252.26 13042 2050.5
## - is_first_child:transport_means 1 310.96 13605 2051.4
## + parent_educ:practice_sport 10 177.52 13116 2051.9
## + ethnic_group:wkly_study_hours 8 70.38 13223 2052.7
## + parent_educ:wkly_study_hours 10 149.49 13144 2053.1
## + parent_educ:parent_marital_status 15 305.22 12988 2056.1
##
## Step: AIC=2033.39
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## transport_means:reading_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 34.43 13364 2030.9
## - lunch_type:test_prep 1 0.02 13330 2031.4
## - lunch_type:writing_score 1 0.02 13330 2031.4
## - lunch_type:reading_score 1 0.10 13330 2031.4
## - transport_means:reading_score 1 0.27 13330 2031.4
## - gender:is_first_child 1 0.36 13330 2031.4
## - parent_educ:test_prep 5 182.37 13512 2031.4
## - gender:lunch_type 1 0.41 13330 2031.4
## - is_first_child:reading_score 1 0.86 13330 2031.4
## - test_prep:writing_score 1 1.16 13331 2031.4
## - lunch_type:parent_marital_status 2 47.31 13377 2031.5
## - test_prep:reading_score 1 2.38 13332 2031.5
## - gender:transport_means 1 2.83 13332 2031.5
## - lunch_type:transport_means 1 4.29 13334 2031.6
## - test_prep:is_first_child 1 5.38 13335 2031.6
## - test_prep:wkly_study_hours 2 52.10 13382 2031.7
## - is_first_child:writing_score 1 8.99 13338 2031.8
## - gender:reading_score 1 9.57 13339 2031.8
## - transport_means:writing_score 1 10.71 13340 2031.9
## - gender:test_prep 1 12.74 13342 2032.0
## - wkly_study_hours:writing_score 2 64.66 13394 2032.2
## - lunch_type:practice_sport 2 68.01 13398 2032.4
## - lunch_type:wkly_study_hours 2 87.17 13417 2033.2
## - ethnic_group:test_prep 4 180.69 13510 2033.3
## - writing_score:reading_score 1 44.61 13374 2033.4
## <none> 13330 2033.4
## - gender:writing_score 1 47.67 13377 2033.5
## - test_prep:parent_marital_status 3 153.56 13483 2034.2
## - parent_educ:transport_means 5 254.65 13584 2034.6
## - parent_marital_status:practice_sport 5 265.85 13595 2035.0
## + practice_sport:transport_means 2 43.34 13286 2035.5
## - wkly_study_hours:reading_score 2 149.95 13480 2036.0
## + gender:wkly_study_hours 2 19.75 13310 2036.5
## + transport_means:wkly_study_hours 2 14.37 13315 2036.8
## + gender:practice_sport 2 12.75 13317 2036.8
## - parent_educ:is_first_child 5 308.70 13638 2036.9
## + test_prep:practice_sport 2 7.10 13322 2037.1
## + parent_marital_status:transport_means 3 43.84 13286 2037.5
## + parent_educ:lunch_type 5 132.91 13197 2037.5
## - test_prep:transport_means 1 145.18 13475 2037.8
## + gender:ethnic_group 4 77.82 13252 2037.9
## + gender:parent_marital_status 3 32.63 13297 2038.0
## + parent_educ:writing_score 5 118.16 13211 2038.1
## + parent_educ:reading_score 5 113.69 13216 2038.3
## + parent_marital_status:is_first_child 3 20.53 13309 2038.5
## + ethnic_group:lunch_type 4 62.42 13267 2038.6
## + parent_marital_status:writing_score 3 11.65 13318 2038.9
## + parent_marital_status:reading_score 3 8.91 13321 2039.0
## - ethnic_group:is_first_child 4 312.27 13642 2039.1
## + ethnic_group:transport_means 4 51.18 13278 2039.1
## - is_first_child:wkly_study_hours 2 223.45 13553 2039.2
## - practice_sport:reading_score 2 225.25 13555 2039.3
## - practice_sport:writing_score 2 234.98 13564 2039.7
## + ethnic_group:writing_score 4 35.77 13294 2039.8
## + ethnic_group:reading_score 4 28.75 13301 2040.1
## - lunch_type:is_first_child 1 209.39 13539 2040.6
## + gender:parent_educ 5 50.49 13279 2041.2
## + practice_sport:wkly_study_hours 4 3.07 13326 2041.3
## + parent_marital_status:wkly_study_hours 6 86.77 13243 2041.5
## + ethnic_group:practice_sport 8 151.47 13178 2042.7
## + ethnic_group:parent_educ 20 666.95 12663 2043.1
## + ethnic_group:parent_marital_status 11 248.72 13081 2044.3
## - is_first_child:transport_means 1 305.28 13635 2044.8
## + parent_educ:practice_sport 10 183.02 13146 2045.2
## + ethnic_group:wkly_study_hours 8 72.08 13257 2046.2
## + parent_educ:wkly_study_hours 10 151.79 13178 2046.6
## + parent_educ:parent_marital_status 15 311.64 13018 2049.4
##
## Step: AIC=2030.91
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:parent_marital_status 2 36.60 13401 2028.5
## - lunch_type:writing_score 1 0.00 13364 2028.9
## - lunch_type:test_prep 1 0.02 13364 2028.9
## - lunch_type:reading_score 1 0.02 13364 2028.9
## - gender:lunch_type 1 0.04 13364 2028.9
## - gender:is_first_child 1 0.15 13364 2028.9
## - transport_means:reading_score 1 0.60 13365 2028.9
## - test_prep:writing_score 1 1.39 13365 2029.0
## - gender:transport_means 1 2.51 13366 2029.0
## - test_prep:reading_score 1 2.58 13366 2029.0
## - lunch_type:transport_means 1 3.50 13368 2029.1
## - is_first_child:reading_score 1 3.54 13368 2029.1
## - test_prep:is_first_child 1 4.34 13368 2029.1
## - test_prep:wkly_study_hours 2 54.29 13418 2029.3
## - transport_means:writing_score 1 9.02 13373 2029.3
## - gender:reading_score 1 9.82 13374 2029.3
## - gender:test_prep 1 11.79 13376 2029.4
## - is_first_child:writing_score 1 15.71 13380 2029.6
## - parent_educ:test_prep 5 200.59 13565 2029.7
## - wkly_study_hours:writing_score 2 63.99 13428 2029.7
## - lunch_type:practice_sport 2 70.02 13434 2030.0
## - lunch_type:wkly_study_hours 2 79.29 13443 2030.4
## - ethnic_group:test_prep 4 175.35 13539 2030.6
## <none> 13364 2030.9
## - writing_score:reading_score 1 45.82 13410 2030.9
## - gender:writing_score 1 48.31 13412 2031.0
## - test_prep:parent_marital_status 3 143.50 13508 2031.2
## - parent_marital_status:practice_sport 5 255.60 13620 2032.1
## - parent_educ:transport_means 5 259.50 13624 2032.3
## + practice_sport:transport_means 2 44.73 13319 2032.9
## - wkly_study_hours:reading_score 2 146.97 13511 2033.4
## + practice_sport:is_first_child 2 34.43 13330 2033.4
## + gender:wkly_study_hours 2 21.76 13342 2034.0
## - parent_educ:is_first_child 5 302.38 13666 2034.1
## + transport_means:wkly_study_hours 2 16.34 13348 2034.2
## + gender:practice_sport 2 16.31 13348 2034.2
## + test_prep:practice_sport 2 4.73 13359 2034.7
## + parent_educ:lunch_type 5 131.56 13232 2035.1
## + parent_marital_status:transport_means 3 39.56 13324 2035.2
## + gender:parent_marital_status 3 37.39 13327 2035.3
## - test_prep:transport_means 1 147.85 13512 2035.4
## + gender:ethnic_group 4 76.43 13288 2035.5
## + parent_marital_status:is_first_child 3 25.62 13338 2035.8
## + parent_educ:writing_score 5 115.23 13249 2035.8
## + parent_educ:reading_score 5 109.11 13255 2036.1
## + ethnic_group:lunch_type 4 58.19 13306 2036.3
## + parent_marital_status:writing_score 3 11.87 13352 2036.4
## + parent_marital_status:reading_score 3 8.66 13355 2036.5
## - is_first_child:wkly_study_hours 2 221.96 13586 2036.6
## - ethnic_group:is_first_child 4 316.00 13680 2036.7
## + ethnic_group:transport_means 4 49.80 13314 2036.7
## + ethnic_group:writing_score 4 34.87 13329 2037.4
## - practice_sport:reading_score 2 243.52 13608 2037.6
## - lunch_type:is_first_child 1 200.99 13565 2037.7
## + ethnic_group:reading_score 4 26.35 13338 2037.8
## - practice_sport:writing_score 2 255.02 13619 2038.1
## + gender:parent_educ 5 52.34 13312 2038.6
## + practice_sport:wkly_study_hours 4 4.83 13359 2038.7
## + parent_marital_status:wkly_study_hours 6 81.30 13283 2039.3
## + ethnic_group:parent_educ 20 680.64 12683 2040.1
## + ethnic_group:practice_sport 8 144.13 13220 2040.5
## + ethnic_group:parent_marital_status 11 244.59 13119 2042.0
## - is_first_child:transport_means 1 302.40 13666 2042.1
## + parent_educ:practice_sport 10 180.37 13184 2042.9
## + ethnic_group:wkly_study_hours 8 69.56 13294 2043.8
## + parent_educ:wkly_study_hours 10 150.71 13213 2044.2
## + parent_educ:parent_marital_status 15 292.93 13071 2047.8
##
## Step: AIC=2028.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## lunch_type:writing_score + lunch_type:reading_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:reading_score 1 0.02 13401 2026.5
## - lunch_type:test_prep 1 0.08 13401 2026.5
## - lunch_type:writing_score 1 0.10 13401 2026.5
## - gender:lunch_type 1 0.14 13401 2026.5
## - gender:is_first_child 1 0.27 13401 2026.5
## - transport_means:reading_score 1 0.31 13401 2026.5
## - gender:transport_means 1 1.75 13402 2026.6
## - test_prep:writing_score 1 1.77 13402 2026.6
## - is_first_child:reading_score 1 1.82 13402 2026.6
## - test_prep:reading_score 1 2.65 13403 2026.7
## - lunch_type:transport_means 1 3.16 13404 2026.7
## - test_prep:wkly_study_hours 2 51.47 13452 2026.8
## - test_prep:is_first_child 1 6.34 13407 2026.8
## - gender:test_prep 1 8.88 13409 2026.9
## - transport_means:writing_score 1 10.11 13411 2027.0
## - gender:reading_score 1 11.14 13412 2027.0
## - is_first_child:writing_score 1 11.68 13412 2027.0
## - wkly_study_hours:writing_score 2 63.57 13464 2027.3
## - parent_educ:test_prep 5 202.60 13603 2027.4
## - lunch_type:practice_sport 2 78.52 13479 2028.0
## - ethnic_group:test_prep 4 171.17 13572 2028.0
## - parent_marital_status:practice_sport 6 265.02 13666 2028.1
## - lunch_type:wkly_study_hours 2 83.97 13484 2028.2
## - writing_score:reading_score 1 44.86 13445 2028.5
## <none> 13401 2028.5
## - gender:writing_score 1 51.15 13452 2028.8
## - test_prep:parent_marital_status 3 145.94 13546 2028.9
## - parent_educ:transport_means 5 257.95 13658 2029.8
## + practice_sport:transport_means 2 45.88 13355 2030.5
## + lunch_type:parent_marital_status 2 36.60 13364 2030.9
## - wkly_study_hours:reading_score 2 147.65 13548 2031.0
## + practice_sport:is_first_child 2 23.73 13377 2031.5
## + gender:wkly_study_hours 2 17.82 13383 2031.7
## - parent_educ:is_first_child 5 308.05 13709 2031.9
## + transport_means:wkly_study_hours 2 13.15 13387 2032.0
## + gender:practice_sport 2 13.06 13388 2032.0
## + test_prep:practice_sport 2 4.51 13396 2032.3
## + parent_educ:lunch_type 5 137.66 13263 2032.4
## + gender:parent_marital_status 3 41.74 13359 2032.7
## - test_prep:transport_means 1 145.91 13546 2032.9
## + parent_marital_status:transport_means 3 36.34 13364 2032.9
## + parent_marital_status:is_first_child 3 28.15 13372 2033.3
## + parent_educ:writing_score 5 115.88 13285 2033.4
## + parent_educ:reading_score 5 112.89 13288 2033.5
## + gender:ethnic_group 4 67.63 13333 2033.5
## + parent_marital_status:writing_score 3 19.31 13381 2033.7
## - is_first_child:wkly_study_hours 2 209.87 13610 2033.7
## + parent_marital_status:reading_score 3 18.33 13382 2033.7
## + ethnic_group:lunch_type 4 57.37 13343 2034.0
## - ethnic_group:is_first_child 4 319.51 13720 2034.4
## + ethnic_group:transport_means 4 46.47 13354 2034.5
## - practice_sport:reading_score 2 237.01 13638 2034.9
## + ethnic_group:writing_score 4 35.08 13366 2035.0
## - lunch_type:is_first_child 1 194.82 13595 2035.0
## + ethnic_group:reading_score 4 23.81 13377 2035.5
## - practice_sport:writing_score 2 251.75 13652 2035.5
## + practice_sport:wkly_study_hours 4 5.04 13396 2036.3
## + gender:parent_educ 5 45.65 13355 2036.5
## + parent_marital_status:wkly_study_hours 6 76.94 13324 2037.1
## + ethnic_group:parent_educ 20 679.69 12721 2037.8
## + ethnic_group:practice_sport 8 149.05 13252 2037.9
## + ethnic_group:parent_marital_status 11 250.46 13150 2039.4
## - is_first_child:transport_means 1 299.95 13700 2039.6
## + parent_educ:practice_sport 10 178.68 13222 2040.6
## + ethnic_group:wkly_study_hours 8 69.52 13331 2041.5
## + parent_educ:wkly_study_hours 10 140.57 13260 2042.3
## + parent_educ:parent_marital_status 15 286.75 13114 2045.8
##
## Step: AIC=2026.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:test_prep + lunch_type:practice_sport + lunch_type:is_first_child +
## lunch_type:transport_means + lunch_type:wkly_study_hours +
## lunch_type:writing_score + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 0.10 13401 2024.5
## - gender:lunch_type 1 0.15 13401 2024.5
## - gender:is_first_child 1 0.27 13401 2024.5
## - transport_means:reading_score 1 0.30 13401 2024.5
## - lunch_type:writing_score 1 0.33 13401 2024.5
## - test_prep:writing_score 1 1.78 13402 2024.6
## - gender:transport_means 1 1.79 13402 2024.6
## - is_first_child:reading_score 1 1.87 13402 2024.6
## - test_prep:reading_score 1 2.66 13403 2024.7
## - lunch_type:transport_means 1 3.17 13404 2024.7
## - test_prep:wkly_study_hours 2 51.51 13452 2024.8
## - test_prep:is_first_child 1 6.33 13407 2024.8
## - gender:test_prep 1 8.86 13409 2024.9
## - transport_means:writing_score 1 10.30 13411 2025.0
## - gender:reading_score 1 11.12 13412 2025.0
## - is_first_child:writing_score 1 11.87 13412 2025.0
## - wkly_study_hours:writing_score 2 63.86 13464 2025.3
## - parent_educ:test_prep 5 202.61 13603 2025.4
## - ethnic_group:test_prep 4 171.24 13572 2026.0
## - lunch_type:practice_sport 2 79.88 13480 2026.0
## - parent_marital_status:practice_sport 6 265.15 13666 2026.1
## - lunch_type:wkly_study_hours 2 84.14 13485 2026.2
## - writing_score:reading_score 1 44.85 13445 2026.5
## <none> 13401 2026.5
## - gender:writing_score 1 51.14 13452 2026.8
## - test_prep:parent_marital_status 3 145.94 13546 2026.9
## - parent_educ:transport_means 5 257.98 13659 2027.8
## + practice_sport:transport_means 2 45.85 13355 2028.5
## + lunch_type:reading_score 1 0.02 13401 2028.5
## + lunch_type:parent_marital_status 2 36.60 13364 2028.9
## - wkly_study_hours:reading_score 2 148.02 13549 2029.0
## + practice_sport:is_first_child 2 23.74 13377 2029.5
## + gender:wkly_study_hours 2 17.84 13383 2029.7
## + gender:practice_sport 2 13.04 13388 2030.0
## + transport_means:wkly_study_hours 2 12.98 13388 2030.0
## - parent_educ:is_first_child 5 309.07 13710 2030.0
## + test_prep:practice_sport 2 4.50 13396 2030.3
## + parent_educ:lunch_type 5 137.51 13263 2030.4
## + gender:parent_marital_status 3 41.72 13359 2030.7
## - test_prep:transport_means 1 145.99 13547 2030.9
## + parent_marital_status:transport_means 3 36.21 13364 2030.9
## + parent_marital_status:is_first_child 3 28.04 13372 2031.3
## + parent_educ:writing_score 5 115.76 13285 2031.4
## + parent_educ:reading_score 5 112.74 13288 2031.5
## + gender:ethnic_group 4 67.47 13333 2031.5
## + parent_marital_status:writing_score 3 19.29 13381 2031.7
## - is_first_child:wkly_study_hours 2 209.89 13610 2031.7
## + parent_marital_status:reading_score 3 18.30 13382 2031.7
## + ethnic_group:lunch_type 4 55.42 13345 2032.1
## - ethnic_group:is_first_child 4 319.50 13720 2032.4
## + ethnic_group:transport_means 4 46.35 13354 2032.5
## - practice_sport:reading_score 2 237.00 13638 2032.9
## + ethnic_group:writing_score 4 35.00 13366 2033.0
## - lunch_type:is_first_child 1 195.72 13596 2033.1
## + ethnic_group:reading_score 4 23.77 13377 2033.5
## - practice_sport:writing_score 2 251.74 13652 2033.5
## + practice_sport:wkly_study_hours 4 5.05 13396 2034.3
## + gender:parent_educ 5 45.11 13356 2034.5
## + parent_marital_status:wkly_study_hours 6 76.95 13324 2035.1
## + ethnic_group:practice_sport 8 148.88 13252 2035.9
## + ethnic_group:parent_educ 20 677.01 12724 2035.9
## + ethnic_group:parent_marital_status 11 249.41 13151 2037.4
## - is_first_child:transport_means 1 301.81 13702 2037.7
## + parent_educ:practice_sport 10 178.36 13222 2038.6
## + ethnic_group:wkly_study_hours 8 69.48 13331 2039.5
## + parent_educ:wkly_study_hours 10 140.56 13260 2040.3
## + parent_educ:parent_marital_status 15 285.72 13115 2043.8
##
## Step: AIC=2024.53
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:lunch_type + gender:test_prep + gender:is_first_child +
## gender:transport_means + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 0.11 13401 2022.5
## - gender:is_first_child 1 0.28 13401 2022.5
## - transport_means:reading_score 1 0.30 13401 2022.5
## - lunch_type:writing_score 1 0.56 13401 2022.6
## - test_prep:writing_score 1 1.69 13402 2022.6
## - gender:transport_means 1 1.78 13402 2022.6
## - is_first_child:reading_score 1 1.87 13403 2022.6
## - test_prep:reading_score 1 2.63 13403 2022.7
## - lunch_type:transport_means 1 3.07 13404 2022.7
## - test_prep:wkly_study_hours 2 51.73 13452 2022.8
## - test_prep:is_first_child 1 6.37 13407 2022.8
## - gender:test_prep 1 9.60 13410 2023.0
## - transport_means:writing_score 1 10.27 13411 2023.0
## - gender:reading_score 1 11.16 13412 2023.0
## - is_first_child:writing_score 1 11.87 13413 2023.1
## - wkly_study_hours:writing_score 2 63.99 13465 2023.3
## - parent_educ:test_prep 5 202.51 13603 2023.4
## - lunch_type:practice_sport 2 79.98 13481 2024.0
## - parent_marital_status:practice_sport 6 265.09 13666 2024.1
## - ethnic_group:test_prep 4 173.01 13574 2024.1
## - lunch_type:wkly_study_hours 2 84.04 13485 2024.2
## - writing_score:reading_score 1 45.50 13446 2024.5
## <none> 13401 2024.5
## - gender:writing_score 1 51.51 13452 2024.8
## - test_prep:parent_marital_status 3 146.34 13547 2024.9
## - parent_educ:transport_means 5 259.11 13660 2025.8
## + practice_sport:transport_means 2 45.69 13355 2026.5
## + lunch_type:test_prep 1 0.10 13401 2026.5
## + lunch_type:reading_score 1 0.04 13401 2026.5
## + lunch_type:parent_marital_status 2 36.68 13364 2026.9
## - wkly_study_hours:reading_score 2 148.13 13549 2027.0
## + practice_sport:is_first_child 2 23.72 13377 2027.5
## + gender:wkly_study_hours 2 17.79 13383 2027.8
## + gender:practice_sport 2 13.08 13388 2028.0
## + transport_means:wkly_study_hours 2 13.08 13388 2028.0
## - parent_educ:is_first_child 5 312.25 13713 2028.1
## + test_prep:practice_sport 2 4.57 13396 2028.3
## + parent_educ:lunch_type 5 137.51 13263 2028.5
## + gender:parent_marital_status 3 41.25 13359 2028.7
## - test_prep:transport_means 1 145.95 13547 2028.9
## + parent_marital_status:transport_means 3 36.01 13365 2029.0
## + parent_marital_status:is_first_child 3 28.06 13373 2029.3
## + parent_educ:writing_score 5 115.77 13285 2029.4
## + parent_educ:reading_score 5 112.72 13288 2029.5
## + gender:ethnic_group 4 67.34 13333 2029.6
## + parent_marital_status:writing_score 3 19.35 13381 2029.7
## - is_first_child:wkly_study_hours 2 209.83 13610 2029.7
## + parent_marital_status:reading_score 3 18.36 13382 2029.7
## + ethnic_group:lunch_type 4 55.43 13345 2030.1
## - ethnic_group:is_first_child 4 319.51 13720 2030.4
## + ethnic_group:transport_means 4 45.43 13355 2030.5
## - practice_sport:reading_score 2 237.93 13639 2030.9
## + ethnic_group:writing_score 4 34.93 13366 2031.0
## - lunch_type:is_first_child 1 195.93 13597 2031.1
## + ethnic_group:reading_score 4 23.62 13377 2031.5
## - practice_sport:writing_score 2 252.60 13653 2031.5
## + practice_sport:wkly_study_hours 4 5.14 13396 2032.3
## + gender:parent_educ 5 45.20 13356 2032.5
## + parent_marital_status:wkly_study_hours 6 76.90 13324 2033.1
## + ethnic_group:practice_sport 8 147.55 13253 2034.0
## + ethnic_group:parent_educ 20 674.97 12726 2034.0
## + ethnic_group:parent_marital_status 11 248.92 13152 2035.5
## - is_first_child:transport_means 1 303.01 13704 2035.7
## + parent_educ:practice_sport 10 176.98 13224 2036.7
## + ethnic_group:wkly_study_hours 8 69.32 13331 2037.5
## + parent_educ:wkly_study_hours 10 140.65 13260 2038.3
## + parent_educ:parent_marital_status 15 282.38 13118 2042.0
##
## Step: AIC=2022.54
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:is_first_child + gender:transport_means +
## gender:writing_score + gender:reading_score + ethnic_group:test_prep +
## ethnic_group:is_first_child + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 0.29 13401 2020.5
## - transport_means:reading_score 1 0.33 13401 2020.5
## - lunch_type:writing_score 1 0.81 13402 2020.6
## - test_prep:writing_score 1 1.67 13402 2020.6
## - gender:transport_means 1 1.79 13403 2020.6
## - is_first_child:reading_score 1 1.86 13403 2020.6
## - test_prep:reading_score 1 2.61 13403 2020.7
## - lunch_type:transport_means 1 3.02 13404 2020.7
## - test_prep:is_first_child 1 6.41 13407 2020.8
## - test_prep:wkly_study_hours 2 52.04 13453 2020.8
## - gender:test_prep 1 9.96 13411 2021.0
## - transport_means:writing_score 1 10.17 13411 2021.0
## - gender:reading_score 1 11.17 13412 2021.0
## - is_first_child:writing_score 1 11.88 13413 2021.1
## - wkly_study_hours:writing_score 2 64.73 13466 2021.4
## - parent_educ:test_prep 5 202.45 13603 2021.4
## - lunch_type:practice_sport 2 79.87 13481 2022.0
## - parent_marital_status:practice_sport 6 265.66 13666 2022.1
## - ethnic_group:test_prep 4 173.39 13574 2022.1
## - lunch_type:wkly_study_hours 2 84.55 13485 2022.2
## <none> 13401 2022.5
## - writing_score:reading_score 1 45.63 13446 2022.5
## - gender:writing_score 1 52.72 13454 2022.9
## - test_prep:parent_marital_status 3 146.27 13547 2022.9
## - parent_educ:transport_means 5 259.00 13660 2023.8
## + practice_sport:transport_means 2 45.63 13355 2024.5
## + gender:lunch_type 1 0.11 13401 2024.5
## + lunch_type:test_prep 1 0.06 13401 2024.5
## + lunch_type:reading_score 1 0.05 13401 2024.5
## + lunch_type:parent_marital_status 2 36.73 13364 2024.9
## - wkly_study_hours:reading_score 2 149.86 13551 2025.1
## + practice_sport:is_first_child 2 23.30 13378 2025.5
## + gender:wkly_study_hours 2 17.89 13383 2025.8
## + gender:practice_sport 2 13.14 13388 2026.0
## + transport_means:wkly_study_hours 2 13.03 13388 2026.0
## - parent_educ:is_first_child 5 314.56 13715 2026.2
## + test_prep:practice_sport 2 4.54 13396 2026.3
## + parent_educ:lunch_type 5 137.60 13263 2026.5
## + gender:parent_marital_status 3 41.35 13359 2026.7
## - test_prep:transport_means 1 146.19 13547 2026.9
## + parent_marital_status:transport_means 3 36.03 13365 2027.0
## + parent_marital_status:is_first_child 3 28.08 13373 2027.3
## + parent_educ:writing_score 5 115.63 13285 2027.4
## + parent_educ:reading_score 5 112.57 13288 2027.6
## + gender:ethnic_group 4 67.12 13334 2027.6
## + parent_marital_status:writing_score 3 19.30 13382 2027.7
## - is_first_child:wkly_study_hours 2 209.75 13610 2027.7
## + parent_marital_status:reading_score 3 18.35 13382 2027.7
## + ethnic_group:lunch_type 4 55.52 13345 2028.1
## - ethnic_group:is_first_child 4 319.46 13720 2028.4
## + ethnic_group:transport_means 4 45.00 13356 2028.5
## - practice_sport:reading_score 2 237.83 13639 2028.9
## + ethnic_group:writing_score 4 34.30 13366 2029.0
## - lunch_type:is_first_child 1 195.90 13597 2029.1
## + ethnic_group:reading_score 4 23.46 13377 2029.5
## - practice_sport:writing_score 2 252.59 13653 2029.6
## + practice_sport:wkly_study_hours 4 5.10 13396 2030.3
## + gender:parent_educ 5 45.20 13356 2030.5
## + parent_marital_status:wkly_study_hours 6 76.10 13325 2031.2
## + ethnic_group:practice_sport 8 147.59 13253 2032.0
## + ethnic_group:parent_educ 20 675.07 12726 2032.0
## + ethnic_group:parent_marital_status 11 249.02 13152 2033.5
## - is_first_child:transport_means 1 303.18 13704 2033.7
## + parent_educ:practice_sport 10 176.55 13224 2034.7
## + ethnic_group:wkly_study_hours 8 69.43 13331 2035.5
## + parent_educ:wkly_study_hours 10 138.61 13262 2036.4
## + parent_educ:parent_marital_status 15 280.46 13120 2040.1
##
## Step: AIC=2020.55
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + transport_means:reading_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - transport_means:reading_score 1 0.30 13401 2018.6
## - lunch_type:writing_score 1 0.85 13402 2018.6
## - test_prep:writing_score 1 1.63 13403 2018.6
## - gender:transport_means 1 1.78 13403 2018.6
## - is_first_child:reading_score 1 2.10 13403 2018.6
## - test_prep:reading_score 1 2.63 13404 2018.7
## - lunch_type:transport_means 1 3.11 13404 2018.7
## - test_prep:is_first_child 1 6.13 13407 2018.8
## - test_prep:wkly_study_hours 2 52.09 13453 2018.8
## - gender:test_prep 1 10.01 13411 2019.0
## - transport_means:writing_score 1 10.34 13411 2019.0
## - gender:reading_score 1 11.07 13412 2019.0
## - is_first_child:writing_score 1 13.46 13414 2019.1
## - wkly_study_hours:writing_score 2 64.45 13466 2019.4
## - parent_educ:test_prep 5 202.40 13604 2019.4
## - lunch_type:practice_sport 2 80.03 13481 2020.1
## - parent_marital_status:practice_sport 6 265.39 13666 2020.1
## - ethnic_group:test_prep 4 173.41 13574 2020.1
## - lunch_type:wkly_study_hours 2 84.50 13486 2020.3
## - writing_score:reading_score 1 45.36 13446 2020.5
## <none> 13401 2020.5
## - gender:writing_score 1 52.66 13454 2020.9
## - test_prep:parent_marital_status 3 146.27 13547 2021.0
## - parent_educ:transport_means 5 259.51 13661 2021.9
## + gender:is_first_child 1 0.29 13401 2022.5
## + gender:lunch_type 1 0.12 13401 2022.5
## + lunch_type:test_prep 1 0.07 13401 2022.5
## + lunch_type:reading_score 1 0.05 13401 2022.5
## + practice_sport:transport_means 2 45.23 13356 2022.6
## + lunch_type:parent_marital_status 2 36.87 13364 2022.9
## - wkly_study_hours:reading_score 2 149.91 13551 2023.1
## + practice_sport:is_first_child 2 23.06 13378 2023.5
## + gender:wkly_study_hours 2 17.86 13383 2023.8
## + gender:practice_sport 2 13.37 13388 2024.0
## + transport_means:wkly_study_hours 2 13.28 13388 2024.0
## - parent_educ:is_first_child 5 314.98 13716 2024.3
## + test_prep:practice_sport 2 4.37 13397 2024.4
## + parent_educ:lunch_type 5 136.71 13264 2024.5
## + gender:parent_marital_status 3 41.50 13360 2024.7
## - test_prep:transport_means 1 146.02 13547 2025.0
## + parent_marital_status:transport_means 3 35.91 13365 2025.0
## + parent_marital_status:is_first_child 3 28.30 13373 2025.3
## + parent_educ:writing_score 5 115.86 13285 2025.4
## + parent_educ:reading_score 5 112.81 13288 2025.6
## + gender:ethnic_group 4 66.90 13334 2025.6
## + parent_marital_status:writing_score 3 19.31 13382 2025.7
## - is_first_child:wkly_study_hours 2 209.47 13610 2025.7
## + parent_marital_status:reading_score 3 18.31 13383 2025.7
## + ethnic_group:lunch_type 4 54.85 13346 2026.1
## - ethnic_group:is_first_child 4 319.53 13721 2026.5
## + ethnic_group:transport_means 4 45.15 13356 2026.6
## - practice_sport:reading_score 2 237.58 13639 2026.9
## + ethnic_group:writing_score 4 34.51 13367 2027.0
## - lunch_type:is_first_child 1 201.39 13602 2027.3
## + ethnic_group:reading_score 4 23.63 13378 2027.5
## - practice_sport:writing_score 2 252.32 13653 2027.6
## + practice_sport:wkly_study_hours 4 5.14 13396 2028.3
## + gender:parent_educ 5 45.13 13356 2028.6
## + parent_marital_status:wkly_study_hours 6 74.72 13326 2029.2
## + ethnic_group:practice_sport 8 147.69 13253 2030.0
## + ethnic_group:parent_educ 20 670.46 12731 2030.3
## + ethnic_group:parent_marital_status 11 249.28 13152 2031.5
## - is_first_child:transport_means 1 305.24 13706 2031.8
## + parent_educ:practice_sport 10 176.82 13224 2032.7
## + ethnic_group:wkly_study_hours 8 69.67 13331 2033.5
## + parent_educ:wkly_study_hours 10 138.77 13262 2034.4
## + parent_educ:parent_marital_status 15 280.68 13120 2038.1
##
## Step: AIC=2018.56
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:writing_score 1 0.78 13402 2016.6
## - test_prep:writing_score 1 1.90 13403 2016.7
## - is_first_child:reading_score 1 2.11 13404 2016.7
## - gender:transport_means 1 2.15 13404 2016.7
## - test_prep:reading_score 1 3.00 13404 2016.7
## - lunch_type:transport_means 1 3.31 13405 2016.7
## - test_prep:is_first_child 1 6.25 13408 2016.8
## - test_prep:wkly_study_hours 2 51.80 13453 2016.8
## - gender:test_prep 1 10.14 13412 2017.0
## - gender:reading_score 1 11.43 13413 2017.1
## - is_first_child:writing_score 1 13.54 13415 2017.2
## - wkly_study_hours:writing_score 2 64.15 13466 2017.4
## - parent_educ:test_prep 5 202.42 13604 2017.4
## - lunch_type:practice_sport 2 80.54 13482 2018.1
## - ethnic_group:test_prep 4 173.28 13575 2018.1
## - parent_marital_status:practice_sport 6 268.00 13669 2018.2
## - lunch_type:wkly_study_hours 2 85.22 13487 2018.3
## <none> 13401 2018.6
## - writing_score:reading_score 1 45.74 13447 2018.6
## - gender:writing_score 1 53.68 13455 2018.9
## - test_prep:parent_marital_status 3 146.02 13547 2019.0
## - parent_educ:transport_means 5 267.05 13668 2020.2
## + transport_means:reading_score 1 0.30 13401 2020.5
## + gender:is_first_child 1 0.25 13401 2020.5
## + gender:lunch_type 1 0.15 13401 2020.6
## + lunch_type:test_prep 1 0.07 13401 2020.6
## + lunch_type:reading_score 1 0.04 13401 2020.6
## + practice_sport:transport_means 2 45.27 13356 2020.6
## + lunch_type:parent_marital_status 2 36.56 13365 2021.0
## - wkly_study_hours:reading_score 2 149.72 13551 2021.1
## + practice_sport:is_first_child 2 23.23 13378 2021.5
## + gender:wkly_study_hours 2 17.67 13384 2021.8
## + transport_means:wkly_study_hours 2 13.23 13388 2022.0
## + gender:practice_sport 2 13.05 13388 2022.0
## - parent_educ:is_first_child 5 315.01 13716 2022.3
## + test_prep:practice_sport 2 4.44 13397 2022.4
## + parent_educ:lunch_type 5 135.06 13266 2022.6
## + gender:parent_marital_status 3 41.19 13360 2022.8
## + parent_marital_status:transport_means 3 35.46 13366 2023.0
## - transport_means:writing_score 1 153.47 13555 2023.3
## + parent_marital_status:is_first_child 3 28.33 13373 2023.3
## + parent_educ:writing_score 5 116.06 13285 2023.4
## - test_prep:transport_means 1 160.61 13562 2023.6
## + gender:ethnic_group 4 67.17 13334 2023.6
## + parent_educ:reading_score 5 112.21 13289 2023.6
## - is_first_child:wkly_study_hours 2 209.18 13611 2023.7
## + parent_marital_status:writing_score 3 19.23 13382 2023.7
## + parent_marital_status:reading_score 3 18.17 13383 2023.8
## + ethnic_group:lunch_type 4 55.15 13346 2024.1
## - ethnic_group:is_first_child 4 319.71 13721 2024.5
## + ethnic_group:transport_means 4 45.31 13356 2024.6
## + ethnic_group:writing_score 4 34.49 13367 2025.0
## - practice_sport:reading_score 2 241.64 13643 2025.1
## - lunch_type:is_first_child 1 201.69 13603 2025.4
## + ethnic_group:reading_score 4 23.61 13378 2025.5
## - practice_sport:writing_score 2 255.57 13657 2025.7
## + practice_sport:wkly_study_hours 4 5.04 13396 2026.3
## + gender:parent_educ 5 45.33 13356 2026.6
## + parent_marital_status:wkly_study_hours 6 73.70 13328 2027.3
## + ethnic_group:practice_sport 8 147.99 13253 2028.0
## + ethnic_group:parent_educ 20 670.76 12731 2028.3
## + ethnic_group:parent_marital_status 11 249.58 13152 2029.5
## - is_first_child:transport_means 1 305.44 13707 2029.9
## + parent_educ:practice_sport 10 174.59 13227 2030.8
## + ethnic_group:wkly_study_hours 8 69.42 13332 2031.5
## + parent_educ:wkly_study_hours 10 138.74 13263 2032.4
## + parent_educ:parent_marital_status 15 280.74 13121 2036.1
##
## Step: AIC=2016.6
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:writing_score + test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:writing_score 1 1.80 13404 2014.7
## - is_first_child:reading_score 1 2.10 13404 2014.7
## - gender:transport_means 1 2.15 13404 2014.7
## - test_prep:reading_score 1 2.78 13405 2014.7
## - lunch_type:transport_means 1 3.36 13406 2014.8
## - test_prep:is_first_child 1 6.16 13408 2014.9
## - test_prep:wkly_study_hours 2 52.32 13454 2014.9
## - gender:test_prep 1 10.26 13412 2015.0
## - gender:reading_score 1 11.86 13414 2015.1
## - is_first_child:writing_score 1 13.43 13416 2015.2
## - parent_educ:test_prep 5 201.91 13604 2015.4
## - wkly_study_hours:writing_score 2 65.71 13468 2015.5
## - lunch_type:practice_sport 2 80.69 13483 2016.1
## - ethnic_group:test_prep 4 174.00 13576 2016.2
## - lunch_type:wkly_study_hours 2 84.81 13487 2016.3
## - parent_marital_status:practice_sport 6 273.49 13676 2016.5
## <none> 13402 2016.6
## - gender:writing_score 1 54.11 13456 2017.0
## - test_prep:parent_marital_status 3 146.88 13549 2017.0
## - writing_score:reading_score 1 62.07 13464 2017.3
## - parent_educ:transport_means 5 267.75 13670 2018.3
## + lunch_type:writing_score 1 0.78 13401 2018.6
## + lunch_type:reading_score 1 0.60 13402 2018.6
## + gender:lunch_type 1 0.42 13402 2018.6
## + gender:is_first_child 1 0.29 13402 2018.6
## + lunch_type:test_prep 1 0.28 13402 2018.6
## + transport_means:reading_score 1 0.22 13402 2018.6
## + practice_sport:transport_means 2 45.37 13357 2018.6
## + lunch_type:parent_marital_status 2 36.89 13365 2019.0
## - wkly_study_hours:reading_score 2 152.04 13554 2019.2
## + practice_sport:is_first_child 2 23.35 13379 2019.6
## + gender:wkly_study_hours 2 17.26 13385 2019.8
## + transport_means:wkly_study_hours 2 13.34 13389 2020.0
## + gender:practice_sport 2 13.11 13389 2020.0
## - parent_educ:is_first_child 5 315.14 13717 2020.3
## + test_prep:practice_sport 2 4.55 13398 2020.4
## + parent_educ:lunch_type 5 135.48 13267 2020.6
## + gender:parent_marital_status 3 41.62 13360 2020.8
## + parent_marital_status:transport_means 3 36.01 13366 2021.0
## + parent_marital_status:is_first_child 3 28.98 13373 2021.3
## - transport_means:writing_score 1 154.60 13557 2021.4
## + parent_educ:writing_score 5 115.08 13287 2021.5
## + gender:ethnic_group 4 66.83 13335 2021.7
## - is_first_child:wkly_study_hours 2 208.64 13611 2021.7
## + parent_educ:reading_score 5 110.17 13292 2021.7
## - test_prep:transport_means 1 163.34 13566 2021.8
## + parent_marital_status:writing_score 3 18.73 13383 2021.8
## + parent_marital_status:reading_score 3 17.60 13385 2021.8
## + ethnic_group:lunch_type 4 55.53 13347 2022.2
## + ethnic_group:transport_means 4 45.91 13356 2022.6
## - ethnic_group:is_first_child 4 322.31 13724 2022.6
## + ethnic_group:writing_score 4 33.95 13368 2023.1
## - practice_sport:reading_score 2 243.53 13646 2023.2
## + ethnic_group:reading_score 4 22.78 13379 2023.6
## - lunch_type:is_first_child 1 207.00 13609 2023.6
## - practice_sport:writing_score 2 257.04 13659 2023.8
## + practice_sport:wkly_study_hours 4 5.31 13397 2024.4
## + gender:parent_educ 5 44.90 13357 2024.6
## + parent_marital_status:wkly_study_hours 6 73.14 13329 2025.4
## + ethnic_group:practice_sport 8 148.36 13254 2026.0
## + ethnic_group:parent_educ 20 671.07 12731 2026.3
## + ethnic_group:parent_marital_status 11 250.28 13152 2027.5
## - is_first_child:transport_means 1 309.57 13712 2028.1
## + parent_educ:practice_sport 10 174.89 13227 2028.8
## + ethnic_group:wkly_study_hours 8 70.01 13332 2029.5
## + parent_educ:wkly_study_hours 10 138.31 13264 2030.5
## + parent_educ:parent_marital_status 15 281.10 13121 2034.1
##
## Step: AIC=2014.68
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## test_prep:reading_score + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:reading_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:reading_score 1 1.48 13405 2012.7
## - is_first_child:reading_score 1 1.63 13406 2012.8
## - gender:transport_means 1 2.34 13406 2012.8
## - lunch_type:transport_means 1 3.39 13407 2012.8
## - test_prep:is_first_child 1 6.16 13410 2013.0
## - test_prep:wkly_study_hours 2 52.00 13456 2013.0
## - gender:reading_score 1 11.46 13415 2013.2
## - is_first_child:writing_score 1 12.46 13416 2013.2
## - gender:test_prep 1 12.89 13417 2013.2
## - parent_educ:test_prep 5 200.38 13604 2013.4
## - wkly_study_hours:writing_score 2 67.14 13471 2013.6
## - lunch_type:practice_sport 2 79.31 13483 2014.2
## - lunch_type:wkly_study_hours 2 84.80 13489 2014.4
## - parent_marital_status:practice_sport 6 274.52 13678 2014.6
## <none> 13404 2014.7
## - gender:writing_score 1 53.43 13457 2015.0
## - ethnic_group:test_prep 4 193.39 13597 2015.1
## - test_prep:parent_marital_status 3 150.75 13555 2015.3
## - writing_score:reading_score 1 60.73 13465 2015.3
## - parent_educ:transport_means 5 268.91 13673 2016.4
## + test_prep:writing_score 1 1.80 13402 2016.6
## + practice_sport:transport_means 2 46.67 13357 2016.6
## + lunch_type:writing_score 1 0.68 13403 2016.7
## + lunch_type:reading_score 1 0.54 13403 2016.7
## + transport_means:reading_score 1 0.46 13404 2016.7
## + gender:lunch_type 1 0.37 13404 2016.7
## + gender:is_first_child 1 0.24 13404 2016.7
## + lunch_type:test_prep 1 0.10 13404 2016.7
## + lunch_type:parent_marital_status 2 36.97 13367 2017.0
## - wkly_study_hours:reading_score 2 155.27 13559 2017.5
## + practice_sport:is_first_child 2 23.61 13380 2017.6
## + gender:wkly_study_hours 2 16.79 13387 2017.9
## + transport_means:wkly_study_hours 2 13.53 13390 2018.1
## + gender:practice_sport 2 13.12 13391 2018.1
## - parent_educ:is_first_child 5 313.40 13717 2018.3
## + test_prep:practice_sport 2 5.53 13398 2018.4
## + parent_educ:lunch_type 5 135.26 13269 2018.7
## + gender:parent_marital_status 3 42.36 13362 2018.8
## + parent_marital_status:transport_means 3 35.66 13368 2019.1
## - transport_means:writing_score 1 152.97 13557 2019.4
## + parent_marital_status:is_first_child 3 28.97 13375 2019.4
## + gender:ethnic_group 4 67.38 13337 2019.7
## + parent_educ:writing_score 5 110.59 13293 2019.8
## - is_first_child:wkly_study_hours 2 209.20 13613 2019.8
## - test_prep:transport_means 1 163.34 13567 2019.8
## + parent_marital_status:writing_score 3 18.60 13385 2019.9
## + parent_marital_status:reading_score 3 17.26 13387 2019.9
## + parent_educ:reading_score 5 106.92 13297 2020.0
## + ethnic_group:lunch_type 4 55.27 13349 2020.2
## - ethnic_group:is_first_child 4 321.63 13726 2020.7
## + ethnic_group:transport_means 4 43.59 13360 2020.8
## + ethnic_group:writing_score 4 34.31 13370 2021.2
## - practice_sport:reading_score 2 243.55 13648 2021.3
## + ethnic_group:reading_score 4 22.60 13381 2021.7
## - lunch_type:is_first_child 1 206.88 13611 2021.7
## - practice_sport:writing_score 2 256.75 13661 2021.9
## + practice_sport:wkly_study_hours 4 5.46 13398 2022.4
## + gender:parent_educ 5 44.77 13359 2022.7
## + parent_marital_status:wkly_study_hours 6 72.82 13331 2023.5
## + ethnic_group:practice_sport 8 147.13 13257 2024.2
## + ethnic_group:parent_educ 20 668.09 12736 2024.5
## + ethnic_group:parent_marital_status 11 252.05 13152 2025.5
## - is_first_child:transport_means 1 313.06 13717 2026.3
## + parent_educ:practice_sport 10 170.36 13234 2027.1
## + ethnic_group:wkly_study_hours 8 70.97 13333 2027.5
## + parent_educ:wkly_study_hours 10 137.80 13266 2028.6
## + parent_educ:parent_marital_status 15 281.80 13122 2032.1
##
## Step: AIC=2012.74
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:reading_score + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:reading_score 1 1.32 13407 2010.8
## - gender:transport_means 1 2.24 13408 2010.8
## - lunch_type:transport_means 1 3.50 13409 2010.9
## - test_prep:is_first_child 1 6.72 13412 2011.0
## - test_prep:wkly_study_hours 2 53.19 13459 2011.1
## - gender:test_prep 1 11.43 13417 2011.2
## - is_first_child:writing_score 1 11.68 13417 2011.3
## - gender:reading_score 1 11.96 13417 2011.3
## - parent_educ:test_prep 5 199.26 13605 2011.5
## - wkly_study_hours:writing_score 2 68.28 13474 2011.7
## - lunch_type:practice_sport 2 79.01 13484 2012.2
## - lunch_type:wkly_study_hours 2 84.35 13490 2012.4
## - parent_marital_status:practice_sport 6 274.75 13680 2012.7
## <none> 13405 2012.7
## - gender:writing_score 1 53.22 13459 2013.1
## - ethnic_group:test_prep 4 193.34 13599 2013.2
## - test_prep:parent_marital_status 3 149.39 13555 2013.3
## - writing_score:reading_score 1 78.86 13484 2014.2
## - parent_educ:transport_means 5 270.25 13676 2014.5
## + practice_sport:transport_means 2 47.08 13358 2014.7
## + test_prep:reading_score 1 1.48 13404 2014.7
## + transport_means:reading_score 1 0.55 13405 2014.7
## + test_prep:writing_score 1 0.50 13405 2014.7
## + lunch_type:writing_score 1 0.45 13405 2014.7
## + lunch_type:test_prep 1 0.41 13405 2014.7
## + gender:is_first_child 1 0.39 13405 2014.7
## + gender:lunch_type 1 0.31 13405 2014.7
## + lunch_type:reading_score 1 0.30 13405 2014.7
## + lunch_type:parent_marital_status 2 36.37 13369 2015.1
## - wkly_study_hours:reading_score 2 157.93 13563 2015.7
## + practice_sport:is_first_child 2 23.45 13382 2015.7
## + gender:wkly_study_hours 2 17.05 13388 2016.0
## + transport_means:wkly_study_hours 2 14.14 13391 2016.1
## + gender:practice_sport 2 13.30 13392 2016.2
## + test_prep:practice_sport 2 5.51 13400 2016.5
## - parent_educ:is_first_child 5 318.31 13724 2016.6
## + parent_educ:lunch_type 5 134.20 13271 2016.8
## + gender:parent_marital_status 3 43.04 13362 2016.8
## + parent_marital_status:transport_means 3 36.04 13369 2017.2
## + parent_marital_status:is_first_child 3 29.52 13376 2017.4
## - transport_means:writing_score 1 157.82 13563 2017.7
## + gender:ethnic_group 4 66.04 13339 2017.8
## + parent_educ:writing_score 5 110.79 13295 2017.8
## - is_first_child:wkly_study_hours 2 209.58 13615 2017.9
## - test_prep:transport_means 1 164.22 13570 2017.9
## + parent_marital_status:writing_score 3 18.30 13387 2017.9
## + parent_marital_status:reading_score 3 16.89 13389 2018.0
## + parent_educ:reading_score 5 107.28 13298 2018.0
## + ethnic_group:lunch_type 4 55.80 13350 2018.3
## + ethnic_group:transport_means 4 43.00 13362 2018.8
## - ethnic_group:is_first_child 4 324.69 13730 2018.9
## + ethnic_group:writing_score 4 33.39 13372 2019.3
## - practice_sport:reading_score 2 243.58 13649 2019.4
## - lunch_type:is_first_child 1 206.22 13612 2019.8
## + ethnic_group:reading_score 4 20.87 13385 2019.8
## - practice_sport:writing_score 2 258.40 13664 2020.0
## + practice_sport:wkly_study_hours 4 5.46 13400 2020.5
## + gender:parent_educ 5 43.20 13362 2020.8
## + parent_marital_status:wkly_study_hours 6 72.52 13333 2021.5
## + ethnic_group:practice_sport 8 148.07 13257 2022.2
## + ethnic_group:parent_educ 20 669.54 12736 2022.5
## + ethnic_group:parent_marital_status 11 252.99 13152 2023.5
## - is_first_child:transport_means 1 315.45 13721 2024.5
## + parent_educ:practice_sport 10 170.06 13235 2025.2
## + ethnic_group:wkly_study_hours 8 72.01 13333 2025.6
## + parent_educ:wkly_study_hours 10 138.74 13267 2026.6
## + parent_educ:parent_marital_status 15 282.44 13123 2030.2
##
## Step: AIC=2010.8
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:transport_means + gender:writing_score +
## gender:reading_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 2.06 13409 2008.9
## - lunch_type:transport_means 1 3.14 13410 2008.9
## - test_prep:wkly_study_hours 2 52.37 13459 2009.1
## - test_prep:is_first_child 1 8.30 13415 2009.2
## - gender:test_prep 1 10.98 13418 2009.3
## - gender:reading_score 1 11.21 13418 2009.3
## - parent_educ:test_prep 5 199.40 13606 2009.5
## - wkly_study_hours:writing_score 2 67.61 13474 2009.8
## - lunch_type:practice_sport 2 79.15 13486 2010.3
## - lunch_type:wkly_study_hours 2 84.09 13491 2010.5
## - parent_marital_status:practice_sport 6 274.31 13681 2010.8
## <none> 13407 2010.8
## - gender:writing_score 1 51.99 13459 2011.1
## - ethnic_group:test_prep 4 192.05 13599 2011.2
## - test_prep:parent_marital_status 3 148.25 13555 2011.3
## - is_first_child:writing_score 1 64.27 13471 2011.6
## - writing_score:reading_score 1 78.91 13486 2012.3
## - parent_educ:transport_means 5 269.60 13676 2012.5
## + practice_sport:transport_means 2 47.48 13359 2012.7
## + is_first_child:reading_score 1 1.32 13405 2012.7
## + test_prep:reading_score 1 1.17 13406 2012.8
## + gender:is_first_child 1 0.59 13406 2012.8
## + transport_means:reading_score 1 0.52 13406 2012.8
## + lunch_type:writing_score 1 0.47 13406 2012.8
## + test_prep:writing_score 1 0.41 13406 2012.8
## + lunch_type:test_prep 1 0.40 13406 2012.8
## + gender:lunch_type 1 0.32 13406 2012.8
## + lunch_type:reading_score 1 0.28 13406 2012.8
## + lunch_type:parent_marital_status 2 35.04 13372 2013.3
## - wkly_study_hours:reading_score 2 157.14 13564 2013.7
## + practice_sport:is_first_child 2 24.67 13382 2013.7
## + gender:wkly_study_hours 2 16.60 13390 2014.1
## + transport_means:wkly_study_hours 2 13.64 13393 2014.2
## + gender:practice_sport 2 13.42 13393 2014.2
## + test_prep:practice_sport 2 5.30 13402 2014.6
## - parent_educ:is_first_child 5 318.85 13726 2014.7
## + parent_educ:lunch_type 5 135.30 13272 2014.8
## + gender:parent_marital_status 3 42.77 13364 2014.9
## + parent_marital_status:transport_means 3 36.64 13370 2015.2
## + parent_marital_status:is_first_child 3 29.83 13377 2015.5
## - transport_means:writing_score 1 156.59 13563 2015.7
## + parent_educ:writing_score 5 111.81 13295 2015.9
## + gender:ethnic_group 4 66.37 13340 2015.9
## - is_first_child:wkly_study_hours 2 208.33 13615 2015.9
## - test_prep:transport_means 1 163.89 13571 2016.0
## + parent_marital_status:writing_score 3 18.15 13389 2016.0
## + parent_educ:reading_score 5 108.20 13299 2016.0
## + parent_marital_status:reading_score 3 17.03 13390 2016.0
## + ethnic_group:lunch_type 4 55.88 13351 2016.3
## - ethnic_group:is_first_child 4 324.74 13732 2016.9
## + ethnic_group:transport_means 4 41.13 13366 2017.0
## - practice_sport:reading_score 2 242.36 13649 2017.4
## + ethnic_group:writing_score 4 32.30 13374 2017.4
## + ethnic_group:reading_score 4 20.14 13387 2017.9
## - lunch_type:is_first_child 1 208.80 13616 2017.9
## - practice_sport:writing_score 2 257.62 13664 2018.0
## + practice_sport:wkly_study_hours 4 5.13 13402 2018.6
## + gender:parent_educ 5 42.95 13364 2018.9
## + parent_marital_status:wkly_study_hours 6 72.01 13335 2019.6
## + ethnic_group:practice_sport 8 147.83 13259 2020.3
## + ethnic_group:parent_educ 20 669.07 12738 2020.6
## + ethnic_group:parent_marital_status 11 252.79 13154 2021.6
## - is_first_child:transport_means 1 314.70 13722 2022.5
## + parent_educ:practice_sport 10 168.84 13238 2023.3
## + ethnic_group:wkly_study_hours 8 73.14 13334 2023.6
## + parent_educ:wkly_study_hours 10 138.71 13268 2024.7
## + parent_educ:parent_marital_status 15 281.31 13126 2028.3
##
## Step: AIC=2008.89
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 2.47 13411 2007.0
## - test_prep:wkly_study_hours 2 51.52 13460 2007.2
## - test_prep:is_first_child 1 8.32 13417 2007.3
## - gender:reading_score 1 11.05 13420 2007.4
## - gender:test_prep 1 11.75 13421 2007.4
## - parent_educ:test_prep 5 200.48 13609 2007.7
## - wkly_study_hours:writing_score 2 66.63 13476 2007.8
## - lunch_type:practice_sport 2 78.42 13487 2008.3
## - lunch_type:wkly_study_hours 2 84.36 13493 2008.6
## - parent_marital_status:practice_sport 6 272.93 13682 2008.8
## <none> 13409 2008.9
## - gender:writing_score 1 51.66 13460 2009.2
## - ethnic_group:test_prep 4 190.47 13599 2009.2
## - test_prep:parent_marital_status 3 147.01 13556 2009.3
## - is_first_child:writing_score 1 64.36 13473 2009.7
## - writing_score:reading_score 1 78.51 13487 2010.3
## - parent_educ:transport_means 5 270.62 13679 2010.7
## + practice_sport:transport_means 2 47.94 13361 2010.8
## + gender:transport_means 1 2.06 13407 2010.8
## + is_first_child:reading_score 1 1.14 13408 2010.8
## + test_prep:reading_score 1 1.10 13408 2010.8
## + transport_means:reading_score 1 0.97 13408 2010.8
## + gender:is_first_child 1 0.53 13408 2010.9
## + lunch_type:writing_score 1 0.48 13408 2010.9
## + gender:lunch_type 1 0.36 13408 2010.9
## + lunch_type:test_prep 1 0.34 13408 2010.9
## + test_prep:writing_score 1 0.34 13408 2010.9
## + lunch_type:reading_score 1 0.25 13409 2010.9
## + lunch_type:parent_marital_status 2 34.26 13375 2011.4
## - wkly_study_hours:reading_score 2 155.67 13564 2011.7
## + practice_sport:is_first_child 2 24.47 13384 2011.8
## + gender:wkly_study_hours 2 16.66 13392 2012.2
## + transport_means:wkly_study_hours 2 13.48 13395 2012.3
## + gender:practice_sport 2 13.45 13395 2012.3
## + test_prep:practice_sport 2 5.19 13404 2012.7
## - parent_educ:is_first_child 5 316.99 13726 2012.7
## + parent_educ:lunch_type 5 137.01 13272 2012.8
## + gender:parent_marital_status 3 42.45 13366 2013.0
## + parent_marital_status:transport_means 3 36.04 13373 2013.3
## + parent_marital_status:is_first_child 3 28.82 13380 2013.6
## + parent_educ:writing_score 5 112.23 13297 2013.9
## + gender:ethnic_group 4 66.45 13342 2014.0
## - transport_means:writing_score 1 161.84 13571 2014.0
## - test_prep:transport_means 1 162.13 13571 2014.0
## + parent_educ:reading_score 5 109.25 13300 2014.1
## + parent_marital_status:writing_score 3 17.59 13391 2014.1
## - is_first_child:wkly_study_hours 2 211.72 13620 2014.1
## + parent_marital_status:reading_score 3 16.54 13392 2014.2
## + ethnic_group:lunch_type 4 55.13 13354 2014.5
## - ethnic_group:is_first_child 4 322.81 13732 2014.9
## + ethnic_group:transport_means 4 42.43 13366 2015.0
## + ethnic_group:writing_score 4 31.82 13377 2015.5
## - practice_sport:reading_score 2 248.84 13658 2015.7
## + ethnic_group:reading_score 4 20.34 13388 2016.0
## - lunch_type:is_first_child 1 212.26 13621 2016.2
## - practice_sport:writing_score 2 265.02 13674 2016.4
## + practice_sport:wkly_study_hours 4 4.86 13404 2016.7
## + gender:parent_educ 5 43.48 13365 2017.0
## + parent_marital_status:wkly_study_hours 6 71.11 13338 2017.8
## + ethnic_group:practice_sport 8 147.83 13261 2018.3
## + ethnic_group:parent_educ 20 668.14 12741 2018.7
## + ethnic_group:parent_marital_status 11 250.04 13159 2019.8
## - is_first_child:transport_means 1 316.68 13726 2020.7
## + parent_educ:practice_sport 10 170.52 13238 2021.3
## + ethnic_group:wkly_study_hours 8 73.57 13335 2021.7
## + parent_educ:wkly_study_hours 10 139.70 13269 2022.7
## + parent_educ:parent_marital_status 15 274.17 13135 2026.7
##
## Step: AIC=2007
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:is_first_child +
## test_prep:transport_means + test_prep:wkly_study_hours +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:is_first_child 1 7.83 13419 2005.3
## - test_prep:wkly_study_hours 2 55.11 13466 2005.4
## - gender:reading_score 1 10.96 13422 2005.5
## - gender:test_prep 1 11.37 13423 2005.5
## - parent_educ:test_prep 5 203.23 13614 2005.9
## - wkly_study_hours:writing_score 2 68.75 13480 2006.0
## - lunch_type:practice_sport 2 77.17 13488 2006.4
## - lunch_type:wkly_study_hours 2 83.60 13495 2006.7
## - parent_marital_status:practice_sport 6 272.73 13684 2006.9
## <none> 13411 2007.0
## - gender:writing_score 1 51.26 13462 2007.2
## - ethnic_group:test_prep 4 191.80 13603 2007.4
## - test_prep:parent_marital_status 3 146.93 13558 2007.4
## - is_first_child:writing_score 1 63.80 13475 2007.8
## - writing_score:reading_score 1 78.83 13490 2008.5
## - parent_educ:transport_means 5 268.35 13680 2008.7
## + lunch_type:transport_means 1 2.47 13409 2008.9
## + practice_sport:transport_means 2 47.08 13364 2008.9
## + gender:transport_means 1 1.38 13410 2008.9
## + test_prep:reading_score 1 1.23 13410 2009.0
## + transport_means:reading_score 1 1.16 13410 2009.0
## + is_first_child:reading_score 1 0.86 13410 2009.0
## + gender:is_first_child 1 0.61 13411 2009.0
## + lunch_type:writing_score 1 0.50 13411 2009.0
## + test_prep:writing_score 1 0.40 13411 2009.0
## + lunch_type:reading_score 1 0.29 13411 2009.0
## + gender:lunch_type 1 0.28 13411 2009.0
## + lunch_type:test_prep 1 0.20 13411 2009.0
## + lunch_type:parent_marital_status 2 33.97 13377 2009.5
## - wkly_study_hours:reading_score 2 158.85 13570 2010.0
## + practice_sport:is_first_child 2 23.86 13387 2010.0
## + gender:wkly_study_hours 2 16.40 13395 2010.3
## + gender:practice_sport 2 13.58 13398 2010.4
## + transport_means:wkly_study_hours 2 13.07 13398 2010.4
## - parent_educ:is_first_child 5 315.07 13726 2010.7
## + test_prep:practice_sport 2 5.09 13406 2010.8
## + parent_educ:lunch_type 5 138.25 13273 2010.9
## + gender:parent_marital_status 3 42.67 13369 2011.1
## + parent_marital_status:transport_means 3 37.05 13374 2011.4
## + parent_marital_status:is_first_child 3 30.11 13381 2011.7
## - test_prep:transport_means 1 159.71 13571 2012.0
## + gender:ethnic_group 4 67.22 13344 2012.0
## + parent_educ:writing_score 5 111.91 13299 2012.1
## + parent_educ:reading_score 5 109.78 13302 2012.2
## - is_first_child:wkly_study_hours 2 211.06 13622 2012.2
## + parent_marital_status:writing_score 3 17.14 13394 2012.2
## + parent_marital_status:reading_score 3 16.46 13395 2012.3
## - transport_means:writing_score 1 167.14 13578 2012.3
## + ethnic_group:lunch_type 4 54.12 13357 2012.6
## + ethnic_group:transport_means 4 43.26 13368 2013.1
## - ethnic_group:is_first_child 4 325.58 13737 2013.2
## + ethnic_group:writing_score 4 32.57 13379 2013.6
## - practice_sport:reading_score 2 249.61 13661 2013.9
## + ethnic_group:reading_score 4 21.46 13390 2014.1
## - lunch_type:is_first_child 1 210.80 13622 2014.2
## - practice_sport:writing_score 2 265.54 13677 2014.6
## + practice_sport:wkly_study_hours 4 4.60 13407 2014.8
## + gender:parent_educ 5 41.99 13369 2015.2
## + parent_marital_status:wkly_study_hours 6 71.43 13340 2015.8
## + ethnic_group:practice_sport 8 146.02 13265 2016.5
## + ethnic_group:parent_educ 20 669.68 12742 2016.8
## + ethnic_group:parent_marital_status 11 250.32 13161 2017.9
## - is_first_child:transport_means 1 319.62 13731 2018.9
## + parent_educ:practice_sport 10 171.27 13240 2019.4
## + ethnic_group:wkly_study_hours 8 71.34 13340 2019.8
## + parent_educ:wkly_study_hours 10 131.98 13279 2021.2
## + parent_educ:parent_marital_status 15 273.51 13138 2024.8
##
## Step: AIC=2005.34
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 53.70 13473 2003.7
## - gender:reading_score 1 11.36 13430 2003.8
## - gender:test_prep 1 11.83 13431 2003.9
## - parent_educ:test_prep 5 203.93 13623 2004.2
## - wkly_study_hours:writing_score 2 69.53 13489 2004.4
## - lunch_type:practice_sport 2 78.84 13498 2004.8
## - lunch_type:wkly_study_hours 2 82.55 13502 2005.0
## - parent_marital_status:practice_sport 6 274.15 13693 2005.3
## <none> 13419 2005.3
## - ethnic_group:test_prep 4 189.08 13608 2005.6
## - gender:writing_score 1 52.99 13472 2005.7
## - test_prep:parent_marital_status 3 156.45 13576 2006.2
## - is_first_child:writing_score 1 77.51 13497 2006.7
## - writing_score:reading_score 1 78.08 13497 2006.8
## + test_prep:is_first_child 1 7.83 13411 2007.0
## - parent_educ:transport_means 5 272.09 13691 2007.2
## + is_first_child:reading_score 1 2.19 13417 2007.2
## + lunch_type:transport_means 1 1.98 13417 2007.3
## + practice_sport:transport_means 2 47.34 13372 2007.3
## + test_prep:reading_score 1 1.62 13418 2007.3
## + gender:transport_means 1 1.46 13418 2007.3
## + transport_means:reading_score 1 1.41 13418 2007.3
## + test_prep:writing_score 1 0.67 13418 2007.3
## + lunch_type:writing_score 1 0.40 13419 2007.3
## + gender:lunch_type 1 0.32 13419 2007.3
## + lunch_type:test_prep 1 0.29 13419 2007.3
## + lunch_type:reading_score 1 0.21 13419 2007.3
## + gender:is_first_child 1 0.07 13419 2007.3
## + lunch_type:parent_marital_status 2 35.51 13384 2007.8
## + practice_sport:is_first_child 2 23.59 13396 2008.3
## - wkly_study_hours:reading_score 2 160.83 13580 2008.4
## + gender:wkly_study_hours 2 15.13 13404 2008.7
## + gender:practice_sport 2 14.92 13404 2008.7
## + transport_means:wkly_study_hours 2 12.60 13406 2008.8
## - parent_educ:is_first_child 5 310.82 13730 2008.8
## + test_prep:practice_sport 2 5.26 13414 2009.1
## + parent_educ:lunch_type 5 137.40 13282 2009.3
## + gender:parent_marital_status 3 42.03 13377 2009.5
## + parent_marital_status:transport_means 3 38.17 13381 2009.7
## + parent_marital_status:is_first_child 3 30.77 13388 2010.0
## + parent_educ:writing_score 5 115.35 13304 2010.2
## - test_prep:transport_means 1 158.86 13578 2010.3
## + gender:ethnic_group 4 69.04 13350 2010.3
## + parent_educ:reading_score 5 114.12 13305 2010.3
## - is_first_child:wkly_study_hours 2 209.46 13629 2010.5
## + parent_marital_status:writing_score 3 18.00 13401 2010.5
## + parent_marital_status:reading_score 3 17.45 13402 2010.6
## - transport_means:writing_score 1 171.22 13590 2010.8
## + ethnic_group:lunch_type 4 52.25 13367 2011.0
## + ethnic_group:transport_means 4 44.71 13374 2011.4
## - ethnic_group:is_first_child 4 324.09 13743 2011.4
## + ethnic_group:writing_score 4 32.98 13386 2011.9
## - lunch_type:is_first_child 1 204.18 13623 2012.2
## - practice_sport:reading_score 2 250.50 13670 2012.3
## + ethnic_group:reading_score 4 21.79 13397 2012.4
## - practice_sport:writing_score 2 267.00 13686 2013.0
## + practice_sport:wkly_study_hours 4 4.44 13415 2013.2
## + gender:parent_educ 5 44.41 13375 2013.4
## + parent_marital_status:wkly_study_hours 6 69.62 13350 2014.3
## + ethnic_group:parent_educ 20 675.36 12744 2014.9
## + ethnic_group:practice_sport 8 144.87 13274 2014.9
## + ethnic_group:parent_marital_status 11 257.17 13162 2015.9
## - is_first_child:transport_means 1 324.75 13744 2017.5
## + parent_educ:practice_sport 10 171.99 13247 2017.7
## + ethnic_group:wkly_study_hours 8 75.50 13344 2018.0
## + parent_educ:wkly_study_hours 10 133.41 13286 2019.5
## + parent_educ:parent_marital_status 15 274.03 13145 2023.2
##
## Step: AIC=2003.7
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - wkly_study_hours:writing_score 2 37.33 13510 2001.3
## - gender:reading_score 1 12.37 13485 2002.2
## - gender:test_prep 1 13.16 13486 2002.3
## - parent_educ:test_prep 5 205.40 13678 2002.6
## - lunch_type:practice_sport 2 76.12 13549 2003.0
## - parent_marital_status:practice_sport 6 267.68 13740 2003.3
## <none> 13473 2003.7
## - ethnic_group:test_prep 4 185.25 13658 2003.8
## - lunch_type:wkly_study_hours 2 93.74 13567 2003.8
## - gender:writing_score 1 53.84 13527 2004.0
## - test_prep:parent_marital_status 3 152.18 13625 2004.3
## - parent_educ:transport_means 5 256.86 13730 2004.8
## - wkly_study_hours:reading_score 2 120.72 13594 2005.0
## - is_first_child:writing_score 1 75.79 13549 2005.0
## - writing_score:reading_score 1 79.19 13552 2005.2
## + test_prep:wkly_study_hours 2 53.70 13419 2005.3
## + test_prep:is_first_child 1 6.41 13466 2005.4
## + lunch_type:transport_means 1 5.29 13468 2005.5
## + test_prep:reading_score 1 3.13 13470 2005.6
## + practice_sport:transport_means 2 47.51 13425 2005.6
## + test_prep:writing_score 1 1.72 13471 2005.6
## + is_first_child:reading_score 1 0.86 13472 2005.7
## + lunch_type:test_prep 1 0.75 13472 2005.7
## + gender:lunch_type 1 0.72 13472 2005.7
## + lunch_type:writing_score 1 0.70 13472 2005.7
## + gender:transport_means 1 0.52 13472 2005.7
## + transport_means:reading_score 1 0.51 13472 2005.7
## + lunch_type:reading_score 1 0.35 13472 2005.7
## + gender:is_first_child 1 0.19 13473 2005.7
## + lunch_type:parent_marital_status 2 33.50 13439 2006.2
## - parent_educ:is_first_child 5 295.29 13768 2006.5
## + gender:wkly_study_hours 2 24.87 13448 2006.6
## + practice_sport:is_first_child 2 24.03 13449 2006.7
## + gender:practice_sport 2 16.24 13457 2007.0
## + transport_means:wkly_study_hours 2 9.09 13464 2007.3
## + test_prep:practice_sport 2 4.99 13468 2007.5
## + parent_educ:lunch_type 5 137.81 13335 2007.6
## + gender:parent_marital_status 3 45.44 13427 2007.7
## + parent_marital_status:is_first_child 3 34.52 13438 2008.2
## + parent_marital_status:transport_means 3 33.67 13439 2008.2
## - is_first_child:wkly_study_hours 2 201.89 13675 2008.5
## + parent_educ:reading_score 5 118.46 13354 2008.5
## + gender:ethnic_group 4 69.97 13403 2008.6
## - transport_means:writing_score 1 159.47 13632 2008.6
## + parent_educ:writing_score 5 114.34 13358 2008.7
## + parent_marital_status:reading_score 3 21.62 13451 2008.8
## - test_prep:transport_means 1 162.03 13635 2008.8
## + parent_marital_status:writing_score 3 21.04 13452 2008.8
## - ethnic_group:is_first_child 4 306.48 13779 2009.0
## + ethnic_group:lunch_type 4 58.44 13414 2009.1
## + ethnic_group:transport_means 4 45.26 13428 2009.7
## + ethnic_group:writing_score 4 35.20 13438 2010.2
## - practice_sport:reading_score 2 243.69 13716 2010.3
## + ethnic_group:reading_score 4 22.35 13450 2010.7
## - lunch_type:is_first_child 1 209.54 13682 2010.8
## - practice_sport:writing_score 2 264.96 13738 2011.2
## + practice_sport:wkly_study_hours 4 2.31 13470 2011.6
## + gender:parent_educ 5 46.05 13427 2011.7
## + parent_marital_status:wkly_study_hours 6 64.09 13409 2012.9
## + ethnic_group:parent_educ 20 684.31 12788 2013.0
## + ethnic_group:practice_sport 8 143.72 13329 2013.4
## + ethnic_group:parent_marital_status 11 257.93 13215 2014.3
## - is_first_child:transport_means 1 313.76 13787 2015.3
## + ethnic_group:wkly_study_hours 8 90.98 13382 2015.7
## + parent_educ:practice_sport 10 156.88 13316 2016.8
## + parent_educ:wkly_study_hours 10 115.35 13358 2018.6
## + parent_educ:parent_marital_status 15 286.40 13186 2021.0
##
## Step: AIC=2001.33
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:test_prep + gender:writing_score + gender:reading_score +
## ethnic_group:test_prep + ethnic_group:is_first_child + parent_educ:test_prep +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 13.42 13524 1999.9
## - gender:reading_score 1 13.79 13524 1999.9
## - parent_educ:test_prep 5 204.00 13714 2000.2
## - lunch_type:practice_sport 2 80.06 13590 2000.8
## - parent_marital_status:practice_sport 6 273.14 13783 2001.1
## <none> 13510 2001.3
## - lunch_type:wkly_study_hours 2 96.48 13607 2001.5
## - test_prep:parent_marital_status 3 145.52 13656 2001.7
## - gender:writing_score 1 57.21 13567 2001.8
## - ethnic_group:test_prep 4 201.87 13712 2002.1
## - is_first_child:writing_score 1 75.66 13586 2002.6
## - parent_educ:transport_means 5 265.29 13775 2002.8
## - writing_score:reading_score 1 80.66 13591 2002.8
## + test_prep:is_first_child 1 7.12 13503 2003.0
## + lunch_type:transport_means 1 6.06 13504 2003.1
## + test_prep:reading_score 1 3.86 13506 2003.2
## + test_prep:writing_score 1 1.90 13508 2003.2
## + gender:lunch_type 1 1.63 13508 2003.3
## + lunch_type:writing_score 1 1.57 13509 2003.3
## + lunch_type:test_prep 1 0.82 13509 2003.3
## + lunch_type:reading_score 1 0.79 13509 2003.3
## + is_first_child:reading_score 1 0.64 13510 2003.3
## + practice_sport:transport_means 2 46.12 13464 2003.3
## + gender:transport_means 1 0.31 13510 2003.3
## + transport_means:reading_score 1 0.17 13510 2003.3
## + gender:is_first_child 1 0.00 13510 2003.3
## + wkly_study_hours:writing_score 2 37.33 13473 2003.7
## - parent_educ:is_first_child 5 286.46 13797 2003.7
## + gender:wkly_study_hours 2 35.87 13474 2003.8
## + lunch_type:parent_marital_status 2 34.32 13476 2003.8
## + practice_sport:is_first_child 2 22.39 13488 2004.3
## + test_prep:wkly_study_hours 2 21.49 13489 2004.4
## + gender:practice_sport 2 18.48 13492 2004.5
## + transport_means:wkly_study_hours 2 10.34 13500 2004.9
## + test_prep:practice_sport 2 4.56 13506 2005.1
## + gender:parent_marital_status 3 42.69 13467 2005.5
## + parent_educ:lunch_type 5 133.25 13377 2005.5
## - is_first_child:wkly_study_hours 2 192.78 13703 2005.7
## + parent_marital_status:transport_means 3 36.80 13473 2005.7
## + parent_marital_status:is_first_child 3 35.50 13475 2005.8
## + parent_educ:reading_score 5 121.18 13389 2006.0
## + parent_educ:writing_score 5 118.16 13392 2006.2
## + gender:ethnic_group 4 70.08 13440 2006.3
## + parent_marital_status:writing_score 3 23.68 13486 2006.3
## + parent_marital_status:reading_score 3 23.57 13487 2006.3
## - transport_means:writing_score 1 162.52 13673 2006.4
## - test_prep:transport_means 1 162.53 13673 2006.4
## - ethnic_group:is_first_child 4 307.86 13818 2006.6
## + ethnic_group:lunch_type 4 49.27 13461 2007.2
## + ethnic_group:transport_means 4 48.14 13462 2007.2
## - practice_sport:reading_score 2 233.87 13744 2007.5
## + ethnic_group:writing_score 4 36.19 13474 2007.8
## - lunch_type:is_first_child 1 198.77 13709 2008.0
## + ethnic_group:reading_score 4 23.65 13486 2008.3
## - practice_sport:writing_score 2 256.94 13767 2008.5
## + practice_sport:wkly_study_hours 4 5.64 13504 2009.1
## + gender:parent_educ 5 48.27 13462 2009.2
## - wkly_study_hours:reading_score 2 291.10 13801 2009.9
## + ethnic_group:parent_educ 20 689.47 12821 2010.4
## + parent_marital_status:wkly_study_hours 6 55.21 13455 2010.9
## + ethnic_group:practice_sport 8 141.71 13368 2011.1
## + ethnic_group:parent_marital_status 11 257.26 13253 2012.0
## - is_first_child:transport_means 1 309.34 13820 2012.7
## + ethnic_group:wkly_study_hours 8 94.09 13416 2013.2
## + parent_educ:practice_sport 10 159.61 13350 2014.3
## + parent_educ:wkly_study_hours 10 122.06 13388 2016.0
## + parent_educ:parent_marital_status 15 275.73 13234 2019.2
##
## Step: AIC=1999.92
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:writing_score + gender:reading_score + ethnic_group:test_prep +
## ethnic_group:is_first_child + parent_educ:test_prep + parent_educ:is_first_child +
## parent_educ:transport_means + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - gender:reading_score 1 8.80 13532 1998.3
## - parent_educ:test_prep 5 203.39 13727 1998.7
## - lunch_type:practice_sport 2 77.92 13602 1999.3
## - parent_marital_status:practice_sport 6 272.75 13796 1999.7
## <none> 13524 1999.9
## - gender:writing_score 1 45.96 13570 1999.9
## - lunch_type:wkly_study_hours 2 98.25 13622 2000.2
## - test_prep:parent_marital_status 3 146.11 13670 2000.3
## - ethnic_group:test_prep 4 202.57 13726 2000.7
## - parent_educ:transport_means 5 255.28 13779 2001.0
## - is_first_child:writing_score 1 71.14 13595 2001.0
## + gender:test_prep 1 13.42 13510 2001.3
## - writing_score:reading_score 1 82.43 13606 2001.5
## + test_prep:is_first_child 1 7.53 13516 2001.6
## + lunch_type:transport_means 1 5.45 13518 2001.7
## + gender:lunch_type 1 3.10 13520 2001.8
## + practice_sport:transport_means 2 48.27 13475 2001.8
## + lunch_type:writing_score 1 2.09 13522 2001.8
## + lunch_type:reading_score 1 1.20 13522 2001.9
## + lunch_type:test_prep 1 1.17 13522 2001.9
## + gender:transport_means 1 0.72 13523 2001.9
## + test_prep:reading_score 1 0.64 13523 2001.9
## + transport_means:reading_score 1 0.41 13523 2001.9
## + is_first_child:reading_score 1 0.33 13523 2001.9
## + gender:is_first_child 1 0.05 13524 2001.9
## + test_prep:writing_score 1 0.00 13524 2001.9
## + gender:wkly_study_hours 2 38.76 13485 2002.2
## + wkly_study_hours:writing_score 2 37.59 13486 2002.3
## - parent_educ:is_first_child 5 290.36 13814 2002.5
## + lunch_type:parent_marital_status 2 31.99 13492 2002.5
## + test_prep:wkly_study_hours 2 22.59 13501 2002.9
## + practice_sport:is_first_child 2 21.63 13502 2003.0
## + gender:practice_sport 2 17.88 13506 2003.1
## + transport_means:wkly_study_hours 2 10.30 13513 2003.5
## + test_prep:practice_sport 2 4.74 13519 2003.7
## + gender:parent_marital_status 3 41.84 13482 2004.1
## - is_first_child:wkly_study_hours 2 189.66 13713 2004.1
## + parent_educ:lunch_type 5 127.40 13396 2004.3
## + parent_marital_status:transport_means 3 35.70 13488 2004.4
## + parent_marital_status:is_first_child 3 34.22 13489 2004.4
## - transport_means:writing_score 1 153.56 13677 2004.6
## + gender:ethnic_group 4 76.21 13447 2004.6
## - test_prep:transport_means 1 155.98 13680 2004.7
## + parent_educ:reading_score 5 118.40 13405 2004.7
## + parent_marital_status:writing_score 3 25.19 13498 2004.8
## + parent_marital_status:reading_score 3 24.25 13499 2004.9
## + parent_educ:writing_score 5 113.87 13410 2004.9
## - ethnic_group:is_first_child 4 309.93 13834 2005.3
## + ethnic_group:transport_means 4 50.94 13473 2005.7
## + ethnic_group:lunch_type 4 50.63 13473 2005.7
## - practice_sport:reading_score 2 231.35 13755 2005.9
## + ethnic_group:writing_score 4 41.24 13482 2006.1
## - lunch_type:is_first_child 1 195.18 13719 2006.4
## + ethnic_group:reading_score 4 27.18 13496 2006.7
## - practice_sport:writing_score 2 254.99 13779 2006.9
## + practice_sport:wkly_study_hours 4 6.13 13517 2007.7
## + gender:parent_educ 5 48.86 13475 2007.8
## + ethnic_group:parent_educ 20 700.93 12823 2008.5
## - wkly_study_hours:reading_score 2 294.58 13818 2008.6
## + parent_marital_status:wkly_study_hours 6 52.60 13471 2009.6
## + ethnic_group:practice_sport 8 139.38 13384 2009.8
## + ethnic_group:parent_marital_status 11 255.23 13268 2010.7
## - is_first_child:transport_means 1 312.53 13836 2011.4
## + ethnic_group:wkly_study_hours 8 95.89 13428 2011.7
## + parent_educ:practice_sport 10 154.00 13370 2013.2
## + parent_educ:wkly_study_hours 10 122.43 13401 2014.5
## + parent_educ:parent_marital_status 15 276.17 13247 2017.8
##
## Step: AIC=1998.3
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:test_prep + parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:test_prep 5 201.80 13734 1997.0
## - lunch_type:practice_sport 2 78.51 13611 1997.7
## <none> 13532 1998.3
## - test_prep:parent_marital_status 3 144.92 13677 1998.6
## - parent_marital_status:practice_sport 6 291.83 13824 1998.9
## - lunch_type:wkly_study_hours 2 107.76 13640 1999.0
## - parent_educ:transport_means 5 247.50 13780 1999.0
## - ethnic_group:test_prep 4 204.35 13737 1999.2
## - is_first_child:writing_score 1 72.61 13605 1999.5
## - writing_score:reading_score 1 79.38 13612 1999.8
## + gender:reading_score 1 8.80 13524 1999.9
## + gender:test_prep 1 8.43 13524 1999.9
## + test_prep:is_first_child 1 7.75 13525 2000.0
## + lunch_type:transport_means 1 5.48 13527 2000.1
## + practice_sport:transport_means 2 50.70 13482 2000.1
## + gender:lunch_type 1 3.10 13529 2000.2
## + lunch_type:writing_score 1 2.53 13530 2000.2
## + lunch_type:reading_score 1 1.58 13531 2000.2
## + lunch_type:test_prep 1 1.45 13531 2000.2
## + test_prep:reading_score 1 1.43 13531 2000.2
## + transport_means:reading_score 1 0.62 13532 2000.3
## + gender:transport_means 1 0.56 13532 2000.3
## + test_prep:writing_score 1 0.22 13532 2000.3
## + gender:is_first_child 1 0.10 13532 2000.3
## + is_first_child:reading_score 1 0.08 13532 2000.3
## + gender:wkly_study_hours 2 38.91 13494 2000.6
## + wkly_study_hours:writing_score 2 38.70 13494 2000.6
## + lunch_type:parent_marital_status 2 33.64 13499 2000.8
## - parent_educ:is_first_child 5 291.98 13824 2000.9
## + test_prep:wkly_study_hours 2 23.07 13509 2001.3
## + practice_sport:is_first_child 2 21.18 13511 2001.4
## + gender:practice_sport 2 14.72 13518 2001.7
## + transport_means:wkly_study_hours 2 11.73 13521 2001.8
## + test_prep:practice_sport 2 5.03 13527 2002.1
## - is_first_child:wkly_study_hours 2 191.44 13724 2002.6
## + parent_educ:lunch_type 5 130.19 13402 2002.6
## + gender:parent_marital_status 3 38.58 13494 2002.6
## + parent_marital_status:transport_means 3 37.22 13495 2002.7
## + gender:ethnic_group 4 81.97 13450 2002.7
## + parent_marital_status:is_first_child 3 31.57 13501 2002.9
## - transport_means:writing_score 1 153.39 13686 2003.0
## - test_prep:transport_means 1 156.01 13688 2003.1
## + parent_marital_status:writing_score 3 27.13 13505 2003.1
## + parent_marital_status:reading_score 3 25.08 13507 2003.2
## + parent_educ:reading_score 5 114.38 13418 2003.3
## + parent_educ:writing_score 5 110.43 13422 2003.5
## - ethnic_group:is_first_child 4 306.80 13839 2003.5
## - gender:writing_score 1 175.84 13708 2003.9
## + ethnic_group:transport_means 4 52.24 13480 2004.0
## + ethnic_group:lunch_type 4 50.55 13482 2004.1
## - practice_sport:reading_score 2 232.38 13765 2004.3
## + ethnic_group:writing_score 4 40.00 13492 2004.6
## - lunch_type:is_first_child 1 197.44 13730 2004.8
## + ethnic_group:reading_score 4 25.49 13507 2005.2
## - practice_sport:writing_score 2 255.78 13788 2005.3
## + practice_sport:wkly_study_hours 4 5.43 13527 2006.1
## + gender:parent_educ 5 49.96 13482 2006.1
## + ethnic_group:parent_educ 20 697.47 12835 2007.1
## - wkly_study_hours:reading_score 2 298.82 13831 2007.2
## + parent_marital_status:wkly_study_hours 6 54.12 13478 2007.9
## + ethnic_group:practice_sport 8 138.17 13394 2008.2
## + ethnic_group:parent_marital_status 11 248.39 13284 2009.4
## + ethnic_group:wkly_study_hours 8 92.34 13440 2010.3
## - is_first_child:transport_means 1 326.26 13859 2010.4
## + parent_educ:practice_sport 10 141.55 13391 2012.1
## + parent_educ:wkly_study_hours 10 121.33 13411 2013.0
## + parent_educ:parent_marital_status 15 271.46 13261 2016.3
##
## Step: AIC=1997.04
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:practice_sport 2 86.65 13821 1996.8
## <none> 13734 1997.0
## - test_prep:parent_marital_status 3 142.87 13877 1997.1
## - parent_educ:transport_means 5 239.49 13974 1997.2
## - parent_marital_status:practice_sport 6 300.39 14034 1997.8
## - ethnic_group:test_prep 4 211.45 13946 1998.0
## + practice_sport:transport_means 2 63.88 13670 1998.3
## + parent_educ:test_prep 5 201.80 13532 1998.3
## - lunch_type:wkly_study_hours 2 125.52 13860 1998.4
## - is_first_child:writing_score 1 78.87 13813 1998.4
## - writing_score:reading_score 1 82.05 13816 1998.5
## + lunch_type:transport_means 1 8.74 13725 1998.7
## + test_prep:is_first_child 1 8.47 13726 1998.7
## + gender:test_prep 1 8.38 13726 1998.7
## + gender:reading_score 1 7.21 13727 1998.7
## + lunch_type:writing_score 1 1.96 13732 1999.0
## + gender:lunch_type 1 1.34 13733 1999.0
## + lunch_type:reading_score 1 1.24 13733 1999.0
## + gender:transport_means 1 0.74 13733 1999.0
## + transport_means:reading_score 1 0.56 13734 1999.0
## + lunch_type:test_prep 1 0.56 13734 1999.0
## + test_prep:reading_score 1 0.22 13734 1999.0
## + gender:is_first_child 1 0.20 13734 1999.0
## + is_first_child:reading_score 1 0.14 13734 1999.0
## + test_prep:writing_score 1 0.00 13734 1999.0
## - parent_educ:is_first_child 5 285.05 14019 1999.2
## + wkly_study_hours:writing_score 2 36.95 13697 1999.5
## + gender:wkly_study_hours 2 35.80 13698 1999.5
## + lunch_type:parent_marital_status 2 35.79 13698 1999.5
## + practice_sport:is_first_child 2 35.32 13699 1999.5
## + test_prep:wkly_study_hours 2 23.19 13711 2000.0
## - is_first_child:wkly_study_hours 2 166.44 13901 2000.1
## + gender:practice_sport 2 18.54 13716 2000.2
## + transport_means:wkly_study_hours 2 9.96 13724 2000.6
## + test_prep:practice_sport 2 3.44 13731 2000.9
## - test_prep:transport_means 1 136.91 13871 2000.9
## - transport_means:writing_score 1 139.08 13873 2001.0
## + parent_educ:lunch_type 5 136.82 13597 2001.1
## + parent_marital_status:transport_means 3 43.64 13690 2001.2
## + gender:ethnic_group 4 89.08 13645 2001.2
## + parent_marital_status:is_first_child 3 34.73 13699 2001.5
## + parent_marital_status:writing_score 3 29.78 13704 2001.8
## + parent_marital_status:reading_score 3 29.17 13705 2001.8
## + parent_educ:reading_score 5 118.65 13616 2001.9
## + gender:parent_marital_status 3 25.24 13709 2002.0
## - practice_sport:reading_score 2 211.32 13946 2002.0
## - ethnic_group:is_first_child 4 309.13 14043 2002.2
## - gender:writing_score 1 170.68 13905 2002.3
## + parent_educ:writing_score 5 108.51 13626 2002.4
## + ethnic_group:lunch_type 4 53.25 13681 2002.7
## + ethnic_group:transport_means 4 50.59 13684 2002.9
## - practice_sport:writing_score 2 234.46 13969 2003.0
## + ethnic_group:writing_score 4 33.63 13700 2003.6
## + ethnic_group:reading_score 4 23.00 13711 2004.0
## - lunch_type:is_first_child 1 226.97 13961 2004.7
## + practice_sport:wkly_study_hours 4 3.68 13730 2004.9
## + gender:parent_educ 5 42.30 13692 2005.2
## + ethnic_group:parent_educ 20 716.59 13018 2005.4
## - wkly_study_hours:reading_score 2 302.92 14037 2005.9
## + parent_marital_status:wkly_study_hours 6 59.55 13675 2006.5
## + ethnic_group:practice_sport 8 141.57 13593 2006.9
## + ethnic_group:wkly_study_hours 8 92.03 13642 2009.1
## - is_first_child:transport_means 1 337.16 14071 2009.3
## + ethnic_group:parent_marital_status 11 210.71 13523 2009.9
## + parent_educ:practice_sport 10 128.28 13606 2011.5
## + parent_educ:wkly_study_hours 10 122.34 13612 2011.8
## + parent_educ:parent_marital_status 15 268.36 13466 2015.4
##
## Step: AIC=1996.75
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:is_first_child + parent_educ:transport_means +
## lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 232.30 14053 1996.6
## <none> 13821 1996.8
## - parent_marital_status:practice_sport 6 286.41 14107 1996.8
## + lunch_type:practice_sport 2 86.65 13734 1997.0
## - test_prep:parent_marital_status 3 159.55 13980 1997.5
## + parent_educ:test_prep 5 209.94 13611 1997.7
## + practice_sport:transport_means 2 69.40 13751 1997.8
## - lunch_type:wkly_study_hours 2 122.61 13943 1998.0
## - ethnic_group:test_prep 4 218.41 14039 1998.0
## - writing_score:reading_score 1 81.91 13903 1998.2
## + test_prep:is_first_child 1 10.45 13810 1998.3
## - is_first_child:writing_score 1 84.28 13905 1998.3
## + gender:reading_score 1 7.80 13813 1998.4
## + gender:test_prep 1 6.36 13814 1998.5
## - parent_educ:is_first_child 5 277.57 14098 1998.5
## + lunch_type:transport_means 1 6.00 13815 1998.5
## + gender:is_first_child 1 3.02 13818 1998.6
## + lunch_type:writing_score 1 2.15 13819 1998.7
## + lunch_type:test_prep 1 1.01 13820 1998.7
## + lunch_type:reading_score 1 0.77 13820 1998.7
## + transport_means:reading_score 1 0.67 13820 1998.7
## + gender:lunch_type 1 0.62 13820 1998.7
## + gender:transport_means 1 0.48 13820 1998.7
## + is_first_child:reading_score 1 0.29 13820 1998.7
## + test_prep:reading_score 1 0.23 13821 1998.7
## + test_prep:writing_score 1 0.08 13821 1998.7
## + lunch_type:parent_marital_status 2 43.71 13777 1998.9
## + gender:wkly_study_hours 2 43.19 13778 1998.9
## + wkly_study_hours:writing_score 2 40.97 13780 1999.0
## + practice_sport:is_first_child 2 37.68 13783 1999.1
## + test_prep:wkly_study_hours 2 20.94 13800 1999.8
## + gender:practice_sport 2 13.89 13807 2000.2
## + transport_means:wkly_study_hours 2 10.28 13810 2000.3
## - transport_means:writing_score 1 132.58 13953 2000.4
## - is_first_child:wkly_study_hours 2 180.30 14001 2000.4
## + test_prep:practice_sport 2 7.16 13814 2000.4
## - test_prep:transport_means 1 134.58 13955 2000.5
## + gender:ethnic_group 4 95.29 13726 2000.7
## + parent_marital_status:transport_means 3 46.82 13774 2000.7
## - ethnic_group:is_first_child 4 288.87 14110 2001.0
## + parent_marital_status:writing_score 3 41.82 13779 2001.0
## + parent_marital_status:reading_score 3 41.64 13779 2001.0
## - practice_sport:reading_score 2 195.51 14016 2001.0
## + parent_educ:reading_score 5 131.60 13689 2001.1
## + parent_educ:lunch_type 5 121.16 13700 2001.5
## + parent_marital_status:is_first_child 3 25.35 13796 2001.7
## + parent_educ:writing_score 5 117.74 13703 2001.7
## + gender:parent_marital_status 3 22.11 13799 2001.8
## + ethnic_group:transport_means 4 63.16 13758 2002.0
## - practice_sport:writing_score 2 220.63 14041 2002.1
## - gender:writing_score 1 175.20 13996 2002.2
## + ethnic_group:lunch_type 4 44.01 13777 2002.9
## - lunch_type:is_first_child 1 197.04 14018 2003.1
## + ethnic_group:writing_score 4 26.52 13794 2003.6
## + ethnic_group:reading_score 4 17.79 13803 2004.0
## + practice_sport:wkly_study_hours 4 2.00 13819 2004.7
## + gender:parent_educ 5 47.40 13773 2004.7
## - wkly_study_hours:reading_score 2 286.88 14108 2004.9
## + parent_marital_status:wkly_study_hours 6 56.23 13765 2006.3
## + ethnic_group:parent_educ 20 692.34 13128 2006.4
## + ethnic_group:practice_sport 8 143.83 13677 2006.6
## + ethnic_group:wkly_study_hours 8 89.30 13732 2008.9
## + ethnic_group:parent_marital_status 11 224.89 13596 2009.1
## - is_first_child:transport_means 1 353.37 14174 2009.6
## + parent_educ:practice_sport 10 130.21 13691 2011.2
## + parent_educ:wkly_study_hours 10 121.53 13699 2011.5
## + parent_educ:parent_marital_status 15 272.23 13549 2015.0
##
## Step: AIC=1996.58
## math_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + reading_score +
## gender:writing_score + ethnic_group:test_prep + ethnic_group:is_first_child +
## parent_educ:is_first_child + lunch_type:is_first_child +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:transport_means + parent_marital_status:practice_sport +
## practice_sport:writing_score + practice_sport:reading_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + transport_means:writing_score +
## wkly_study_hours:reading_score + writing_score:reading_score
##
## Df Sum of Sq RSS AIC
## <none> 14053 1996.6
## - parent_educ:is_first_child 5 243.00 14296 1996.7
## + parent_educ:transport_means 5 232.30 13821 1996.8
## + lunch_type:practice_sport 2 79.45 13974 1997.2
## - parent_marital_status:practice_sport 6 309.19 14362 1997.4
## - test_prep:parent_marital_status 3 164.69 14218 1997.5
## - transport_means:writing_score 1 71.84 14125 1997.6
## - lunch_type:wkly_study_hours 2 120.40 14174 1997.6
## + test_prep:is_first_child 1 15.23 14038 1997.9
## - is_first_child:writing_score 1 80.30 14133 1997.9
## - writing_score:reading_score 1 82.81 14136 1998.0
## + parent_educ:test_prep 5 199.75 13853 1998.1
## + transport_means:reading_score 1 6.93 14046 1998.3
## + lunch_type:test_prep 1 3.36 14050 1998.4
## + lunch_type:writing_score 1 3.17 14050 1998.5
## + gender:wkly_study_hours 2 50.20 14003 1998.5
## + gender:is_first_child 1 2.46 14051 1998.5
## + gender:test_prep 1 2.33 14051 1998.5
## + wkly_study_hours:writing_score 2 49.45 14004 1998.5
## + lunch_type:reading_score 1 1.51 14052 1998.5
## + gender:transport_means 1 1.34 14052 1998.5
## + is_first_child:reading_score 1 0.90 14052 1998.5
## + gender:lunch_type 1 0.73 14052 1998.5
## + practice_sport:transport_means 2 48.17 14005 1998.6
## + gender:reading_score 1 0.54 14053 1998.6
## + test_prep:reading_score 1 0.41 14053 1998.6
## + lunch_type:transport_means 1 0.09 14053 1998.6
## + test_prep:writing_score 1 0.06 14053 1998.6
## + practice_sport:is_first_child 2 44.89 14008 1998.7
## - ethnic_group:test_prep 4 244.53 14298 1998.8
## + lunch_type:parent_marital_status 2 40.32 14013 1998.9
## - is_first_child:wkly_study_hours 2 159.16 14212 1999.2
## + test_prep:wkly_study_hours 2 13.46 14040 2000.0
## + parent_marital_status:reading_score 3 58.75 13994 2000.1
## - practice_sport:reading_score 2 182.63 14236 2000.2
## + gender:practice_sport 2 8.44 14045 2000.2
## + test_prep:practice_sport 2 5.82 14047 2000.3
## + transport_means:wkly_study_hours 2 5.20 14048 2000.4
## + parent_marital_status:writing_score 3 51.35 14002 2000.4
## - test_prep:transport_means 1 142.53 14196 2000.5
## + parent_marital_status:transport_means 3 41.68 14011 2000.8
## - ethnic_group:is_first_child 4 297.56 14351 2000.9
## + parent_marital_status:is_first_child 3 37.25 14016 2001.0
## + parent_educ:reading_score 5 129.71 13923 2001.1
## + gender:ethnic_group 4 82.34 13971 2001.1
## + gender:parent_marital_status 3 27.68 14025 2001.4
## - practice_sport:writing_score 2 215.10 14268 2001.5
## + parent_educ:lunch_type 5 117.82 13935 2001.6
## + parent_educ:writing_score 5 112.10 13941 2001.9
## - gender:writing_score 1 182.12 14235 2002.2
## - lunch_type:is_first_child 1 186.60 14240 2002.4
## + ethnic_group:transport_means 4 51.34 14002 2002.4
## + ethnic_group:lunch_type 4 44.73 14008 2002.7
## + ethnic_group:writing_score 4 30.89 14022 2003.3
## + ethnic_group:reading_score 4 18.88 14034 2003.8
## - wkly_study_hours:reading_score 2 277.37 14330 2004.1
## + practice_sport:wkly_study_hours 4 7.28 14046 2004.3
## + gender:parent_educ 5 49.63 14004 2004.5
## + ethnic_group:parent_educ 20 721.15 13332 2005.5
## + parent_marital_status:wkly_study_hours 6 65.25 13988 2005.8
## + ethnic_group:practice_sport 8 153.25 13900 2006.1
## + ethnic_group:parent_marital_status 11 262.78 13790 2007.4
## + ethnic_group:wkly_study_hours 8 81.47 13972 2009.2
## - is_first_child:transport_means 1 384.88 14438 2010.5
## + parent_educ:practice_sport 10 135.76 13917 2010.8
## + parent_educ:wkly_study_hours 10 116.54 13937 2011.7
## + parent_educ:parent_marital_status 15 276.02 13777 2014.9summary(stepwise_model_math2)##
## Call:
## lm(formula = math_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + writing_score +
## reading_score + gender:writing_score + ethnic_group:test_prep +
## ethnic_group:is_first_child + parent_educ:is_first_child +
## lunch_type:is_first_child + lunch_type:wkly_study_hours +
## test_prep:parent_marital_status + test_prep:transport_means +
## parent_marital_status:practice_sport + practice_sport:writing_score +
## practice_sport:reading_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:reading_score +
## writing_score:reading_score, data = df_4_mdl_math2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2205 -3.1685 0.1617 3.0255 14.1753
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -3.7732346 6.1060153
## gendermale 19.5037678 2.1350965
## ethnic_groupgroup B 0.0911814 1.9626266
## ethnic_groupgroup C 2.2583221 1.9063393
## ethnic_groupgroup D -2.3065390 1.9766142
## ethnic_groupgroup E 6.8721719 2.0811662
## parent_educbachelor's degree 0.7246770 1.3336275
## parent_educhigh school -0.0376461 1.2401768
## parent_educmaster's degree -5.6191979 1.9393807
## parent_educsome college 0.2438043 1.2155068
## parent_educsome high school 1.5300633 1.2215785
## lunch_typestandard 2.5885838 1.1720655
## test_prepnone 1.4634745 1.9994107
## parent_marital_statusmarried -3.9453199 1.8544617
## parent_marital_statussingle -7.0721210 2.3632601
## parent_marital_statuswidowed 2.3207244 3.6534230
## practice_sportregularly -3.4108699 4.2307260
## practice_sportsometimes -3.8354109 4.1741735
## is_first_childyes -0.9346879 3.0610929
## transport_meansschool_bus 6.8492626 2.4855490
## wkly_study_hours> 10 -6.5941563 3.1856983
## wkly_study_hours10-May -1.6692567 2.5757555
## writing_score 0.3703874 0.1581504
## reading_score 0.3645115 0.1585190
## gendermale:writing_score -0.0801567 0.0306717
## ethnic_groupgroup B:test_prepnone -0.0531441 1.8722180
## ethnic_groupgroup C:test_prepnone -0.0459041 1.7949174
## ethnic_groupgroup D:test_prepnone 3.2520088 1.8564117
## ethnic_groupgroup E:test_prepnone -0.2413349 1.9584231
## ethnic_groupgroup B:is_first_childyes 1.2077538 1.9099819
## ethnic_groupgroup C:is_first_childyes -3.2494575 1.8175354
## ethnic_groupgroup D:is_first_childyes -0.7330669 1.8397464
## ethnic_groupgroup E:is_first_childyes -1.7216009 2.0704415
## parent_educbachelor's degree:is_first_childyes -2.8682520 1.6564331
## parent_educhigh school:is_first_childyes 1.0411100 1.5060373
## parent_educmaster's degree:is_first_childyes 3.3535434 2.2486132
## parent_educsome college:is_first_childyes -0.6354479 1.4852010
## parent_educsome high school:is_first_childyes -0.7064389 1.4850533
## lunch_typestandard:is_first_childyes 2.7993264 1.0582225
## lunch_typestandard:wkly_study_hours> 10 -3.1990455 1.5057795
## lunch_typestandard:wkly_study_hours10-May -1.2823329 1.1408100
## test_prepnone:parent_marital_statusmarried 3.1877010 1.3277750
## test_prepnone:parent_marital_statussingle 3.1318541 1.4967208
## test_prepnone:parent_marital_statuswidowed 1.6334414 3.8228684
## test_prepnone:transport_meansschool_bus -2.2970524 0.9935766
## parent_marital_statusmarried:practice_sportregularly 3.4752009 1.9447658
## parent_marital_statussingle:practice_sportregularly 7.0869988 2.4423040
## parent_marital_statuswidowed:practice_sportregularly -2.8100117 4.9287326
## parent_marital_statusmarried:practice_sportsometimes 2.6438159 1.8543985
## parent_marital_statussingle:practice_sportsometimes 4.8775517 2.3549791
## parent_marital_statuswidowed:practice_sportsometimes -0.0954158 5.2650211
## practice_sportregularly:writing_score 0.3133280 0.1690612
## practice_sportsometimes:writing_score 0.4517201 0.1619272
## practice_sportregularly:reading_score -0.2969884 0.1667680
## practice_sportsometimes:reading_score -0.4161670 0.1602656
## is_first_childyes:transport_meansschool_bus -3.7791725 0.9947473
## is_first_childyes:wkly_study_hours> 10 0.8035222 1.4523725
## is_first_childyes:wkly_study_hours10-May -2.0145800 1.1318191
## is_first_childyes:writing_score 0.0596601 0.0343793
## transport_meansschool_bus:writing_score -0.0500286 0.0304807
## wkly_study_hours> 10:reading_score 0.1510529 0.0470513
## wkly_study_hours10-May:reading_score 0.0722752 0.0366033
## writing_score:reading_score 0.0013020 0.0007388
## t value Pr(>|t|)
## (Intercept) -0.618 0.536873
## gendermale 9.135 < 2e-16 ***
## ethnic_groupgroup B 0.046 0.962962
## ethnic_groupgroup C 1.185 0.236695
## ethnic_groupgroup D -1.167 0.243773
## ethnic_groupgroup E 3.302 0.001025 **
## parent_educbachelor's degree 0.543 0.587093
## parent_educhigh school -0.030 0.975795
## parent_educmaster's degree -2.897 0.003919 **
## parent_educsome college 0.201 0.841106
## parent_educsome high school 1.253 0.210932
## lunch_typestandard 2.209 0.027634 *
## test_prepnone 0.732 0.464523
## parent_marital_statusmarried -2.127 0.033844 *
## parent_marital_statussingle -2.993 0.002896 **
## parent_marital_statuswidowed 0.635 0.525561
## practice_sportregularly -0.806 0.420483
## practice_sportsometimes -0.919 0.358598
## is_first_childyes -0.305 0.760224
## transport_meansschool_bus 2.756 0.006061 **
## wkly_study_hours> 10 -2.070 0.038946 *
## wkly_study_hours10-May -0.648 0.517225
## writing_score 2.342 0.019552 *
## reading_score 2.299 0.021868 *
## gendermale:writing_score -2.613 0.009222 **
## ethnic_groupgroup B:test_prepnone -0.028 0.977365
## ethnic_groupgroup C:test_prepnone -0.026 0.979606
## ethnic_groupgroup D:test_prepnone 1.752 0.080395 .
## ethnic_groupgroup E:test_prepnone -0.123 0.901973
## ethnic_groupgroup B:is_first_childyes 0.632 0.527440
## ethnic_groupgroup C:is_first_childyes -1.788 0.074377 .
## ethnic_groupgroup D:is_first_childyes -0.398 0.690452
## ethnic_groupgroup E:is_first_childyes -0.832 0.406060
## parent_educbachelor's degree:is_first_childyes -1.732 0.083933 .
## parent_educhigh school:is_first_childyes 0.691 0.489687
## parent_educmaster's degree:is_first_childyes 1.491 0.136459
## parent_educsome college:is_first_childyes -0.428 0.668933
## parent_educsome high school:is_first_childyes -0.476 0.634486
## lunch_typestandard:is_first_childyes 2.645 0.008405 **
## lunch_typestandard:wkly_study_hours> 10 -2.125 0.034092 *
## lunch_typestandard:wkly_study_hours10-May -1.124 0.261502
## test_prepnone:parent_marital_statusmarried 2.401 0.016706 *
## test_prepnone:parent_marital_statussingle 2.092 0.036874 *
## test_prepnone:parent_marital_statuswidowed 0.427 0.669349
## test_prepnone:transport_meansschool_bus -2.312 0.021168 *
## parent_marital_statusmarried:practice_sportregularly 1.787 0.074520 .
## parent_marital_statussingle:practice_sportregularly 2.902 0.003866 **
## parent_marital_statuswidowed:practice_sportregularly -0.570 0.568833
## parent_marital_statusmarried:practice_sportsometimes 1.426 0.154547
## parent_marital_statussingle:practice_sportsometimes 2.071 0.038829 *
## parent_marital_statuswidowed:practice_sportsometimes -0.018 0.985548
## practice_sportregularly:writing_score 1.853 0.064392 .
## practice_sportsometimes:writing_score 2.790 0.005468 **
## practice_sportregularly:reading_score -1.781 0.075513 .
## practice_sportsometimes:reading_score -2.597 0.009674 **
## is_first_childyes:transport_meansschool_bus -3.799 0.000162 ***
## is_first_childyes:wkly_study_hours> 10 0.553 0.580328
## is_first_childyes:wkly_study_hours10-May -1.780 0.075660 .
## is_first_childyes:writing_score 1.735 0.083263 .
## transport_meansschool_bus:writing_score -1.641 0.101328
## wkly_study_hours> 10:reading_score 3.210 0.001406 **
## wkly_study_hours10-May:reading_score 1.975 0.048840 *
## writing_score:reading_score 1.762 0.078609 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.164 on 527 degrees of freedom
## Multiple R-squared: 0.9082, Adjusted R-squared: 0.8974
## F-statistic: 84.05 on 62 and 527 DF, p-value: < 2.2e-16REading Score
df_4_mdl_read2=test_df %>% dplyr::select(gender,ethnic_group,parent_educ,lunch_type,test_prep,parent_marital_status,practice_sport,is_first_child,transport_means,wkly_study_hours,reading_score,writing_score,math_score)
full_fit_read2=lm(reading_score ~ .^2,data=df_4_mdl_read2)summary(full_fit_read2)##
## Call:
## lm(formula = reading_score ~ .^2, data = df_4_mdl_read2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.157 -1.999 0.000 2.306 9.448
##
## Coefficients: (6 not defined because of singularities)
## Estimate Std. Error
## (Intercept) -4.426e+00 1.085e+01
## gendermale 1.402e+00 5.240e+00
## ethnic_groupgroup B 7.758e+00 7.293e+00
## ethnic_groupgroup C 7.180e+00 6.787e+00
## ethnic_groupgroup D 4.785e+00 7.198e+00
## ethnic_groupgroup E -2.946e+00 7.445e+00
## parent_educbachelor's degree 4.277e+00 7.073e+00
## parent_educhigh school -1.777e+00 5.329e+00
## parent_educmaster's degree -3.918e+00 9.371e+00
## parent_educsome college 1.329e+00 5.131e+00
## parent_educsome high school -3.048e+00 5.280e+00
## lunch_typestandard 2.687e+00 4.201e+00
## test_prepnone 8.108e-01 4.286e+00
## parent_marital_statusmarried -6.063e+00 5.250e+00
## parent_marital_statussingle -6.355e+00 6.105e+00
## parent_marital_statuswidowed -1.079e+01 1.288e+01
## practice_sportregularly -2.415e+00 6.762e+00
## practice_sportsometimes -3.900e-01 6.671e+00
## is_first_childyes 2.294e+00 3.917e+00
## transport_meansschool_bus 6.181e+00 3.912e+00
## wkly_study_hours> 10 3.133e+00 5.885e+00
## wkly_study_hours10-May 6.200e+00 4.543e+00
## writing_score 9.889e-01 2.891e-01
## math_score 1.925e-02 2.827e-01
## gendermale:ethnic_groupgroup B 2.970e-01 3.012e+00
## gendermale:ethnic_groupgroup C 2.311e+00 2.812e+00
## gendermale:ethnic_groupgroup D 1.262e+00 2.743e+00
## gendermale:ethnic_groupgroup E 1.978e+00 3.266e+00
## gendermale:parent_educbachelor's degree -2.855e+00 2.374e+00
## gendermale:parent_educhigh school -6.166e-01 2.108e+00
## gendermale:parent_educmaster's degree -9.504e+00 4.065e+00
## gendermale:parent_educsome college -3.343e-01 2.169e+00
## gendermale:parent_educsome high school 3.952e-02 2.329e+00
## gendermale:lunch_typestandard -2.115e+00 1.596e+00
## gendermale:test_prepnone -5.253e-01 1.649e+00
## gendermale:parent_marital_statusmarried 2.174e+00 2.136e+00
## gendermale:parent_marital_statussingle -3.874e-01 2.399e+00
## gendermale:parent_marital_statuswidowed 1.051e+00 5.789e+00
## gendermale:practice_sportregularly 3.005e+00 2.716e+00
## gendermale:practice_sportsometimes 4.005e+00 2.621e+00
## gendermale:is_first_childyes -2.639e-01 1.538e+00
## gendermale:transport_meansschool_bus -2.728e-01 1.419e+00
## gendermale:wkly_study_hours> 10 -3.911e+00 2.308e+00
## gendermale:wkly_study_hours10-May -1.622e+00 1.716e+00
## gendermale:writing_score -1.191e-01 8.234e-02
## gendermale:math_score 9.074e-02 7.834e-02
## ethnic_groupgroup B:parent_educbachelor's degree 1.057e+00 4.470e+00
## ethnic_groupgroup C:parent_educbachelor's degree 2.412e+00 4.449e+00
## ethnic_groupgroup D:parent_educbachelor's degree 2.018e+00 4.420e+00
## ethnic_groupgroup E:parent_educbachelor's degree -1.433e+00 5.187e+00
## ethnic_groupgroup B:parent_educhigh school -1.023e+00 2.592e+00
## ethnic_groupgroup C:parent_educhigh school 7.632e-01 2.452e+00
## ethnic_groupgroup D:parent_educhigh school -4.872e-01 2.543e+00
## ethnic_groupgroup E:parent_educhigh school 1.508e+00 2.839e+00
## ethnic_groupgroup B:parent_educmaster's degree 1.676e+01 5.091e+00
## ethnic_groupgroup C:parent_educmaster's degree 1.480e+01 4.727e+00
## ethnic_groupgroup D:parent_educmaster's degree 1.329e+01 4.860e+00
## ethnic_groupgroup E:parent_educmaster's degree 1.189e+01 5.147e+00
## ethnic_groupgroup B:parent_educsome college 5.175e-01 2.898e+00
## ethnic_groupgroup C:parent_educsome college 1.594e+00 2.700e+00
## ethnic_groupgroup D:parent_educsome college 2.192e+00 2.866e+00
## ethnic_groupgroup E:parent_educsome college 6.107e+00 2.860e+00
## ethnic_groupgroup B:parent_educsome high school 3.782e+00 2.779e+00
## ethnic_groupgroup C:parent_educsome high school 3.713e+00 2.558e+00
## ethnic_groupgroup D:parent_educsome high school 2.160e+00 2.604e+00
## ethnic_groupgroup E:parent_educsome high school 7.790e+00 2.829e+00
## ethnic_groupgroup B:lunch_typestandard 3.824e+00 1.950e+00
## ethnic_groupgroup C:lunch_typestandard 4.537e+00 1.862e+00
## ethnic_groupgroup D:lunch_typestandard 6.910e+00 1.871e+00
## ethnic_groupgroup E:lunch_typestandard 2.204e+00 2.181e+00
## ethnic_groupgroup B:test_prepnone -4.163e-01 2.144e+00
## ethnic_groupgroup C:test_prepnone 1.560e+00 2.017e+00
## ethnic_groupgroup D:test_prepnone 5.353e-01 2.054e+00
## ethnic_groupgroup E:test_prepnone 1.851e+00 2.216e+00
## ethnic_groupgroup B:parent_marital_statusmarried 6.731e+00 2.659e+00
## ethnic_groupgroup C:parent_marital_statusmarried 3.053e+00 2.462e+00
## ethnic_groupgroup D:parent_marital_statusmarried 1.614e+00 2.467e+00
## ethnic_groupgroup E:parent_marital_statusmarried 3.724e+00 2.710e+00
## ethnic_groupgroup B:parent_marital_statussingle 8.698e+00 3.046e+00
## ethnic_groupgroup C:parent_marital_statussingle 6.007e+00 2.887e+00
## ethnic_groupgroup D:parent_marital_statussingle 5.892e+00 2.899e+00
## ethnic_groupgroup E:parent_marital_statussingle 1.071e+01 3.238e+00
## ethnic_groupgroup B:parent_marital_statuswidowed -3.566e+01 3.368e+01
## ethnic_groupgroup C:parent_marital_statuswidowed -4.413e+01 2.852e+01
## ethnic_groupgroup D:parent_marital_statuswidowed -1.789e+01 2.687e+01
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly -2.261e+00 3.480e+00
## ethnic_groupgroup C:practice_sportregularly -3.279e+00 3.452e+00
## ethnic_groupgroup D:practice_sportregularly -2.487e+00 3.761e+00
## ethnic_groupgroup E:practice_sportregularly 1.780e+00 3.590e+00
## ethnic_groupgroup B:practice_sportsometimes -4.031e-01 3.680e+00
## ethnic_groupgroup C:practice_sportsometimes -1.435e+00 3.571e+00
## ethnic_groupgroup D:practice_sportsometimes -1.670e+00 3.875e+00
## ethnic_groupgroup E:practice_sportsometimes 1.511e+00 3.614e+00
## ethnic_groupgroup B:is_first_childyes -2.111e+00 1.872e+00
## ethnic_groupgroup C:is_first_childyes -2.717e+00 1.742e+00
## ethnic_groupgroup D:is_first_childyes -2.832e+00 1.786e+00
## ethnic_groupgroup E:is_first_childyes -3.604e+00 2.076e+00
## ethnic_groupgroup B:transport_meansschool_bus -1.703e+00 1.961e+00
## ethnic_groupgroup C:transport_meansschool_bus -9.056e-01 1.760e+00
## ethnic_groupgroup D:transport_meansschool_bus 1.526e+00 1.794e+00
## ethnic_groupgroup E:transport_meansschool_bus 7.194e-01 2.179e+00
## ethnic_groupgroup B:wkly_study_hours> 10 -1.329e+00 3.249e+00
## ethnic_groupgroup C:wkly_study_hours> 10 -1.667e+00 3.237e+00
## ethnic_groupgroup D:wkly_study_hours> 10 -4.543e+00 3.271e+00
## ethnic_groupgroup E:wkly_study_hours> 10 -3.228e+00 3.508e+00
## ethnic_groupgroup B:wkly_study_hours10-May -6.738e-01 2.640e+00
## ethnic_groupgroup C:wkly_study_hours10-May -3.220e+00 2.610e+00
## ethnic_groupgroup D:wkly_study_hours10-May -3.441e+00 2.653e+00
## ethnic_groupgroup E:wkly_study_hours10-May -5.441e+00 2.887e+00
## ethnic_groupgroup B:writing_score -1.839e-01 1.735e-01
## ethnic_groupgroup C:writing_score -4.289e-02 1.648e-01
## ethnic_groupgroup D:writing_score -8.389e-02 1.631e-01
## ethnic_groupgroup E:writing_score -2.687e-02 1.938e-01
## ethnic_groupgroup B:math_score -1.872e-02 1.721e-01
## ethnic_groupgroup C:math_score -1.279e-01 1.578e-01
## ethnic_groupgroup D:math_score -7.158e-02 1.555e-01
## ethnic_groupgroup E:math_score -5.867e-02 1.847e-01
## parent_educbachelor's degree:lunch_typestandard -6.165e-01 1.834e+00
## parent_educhigh school:lunch_typestandard -5.979e-01 1.402e+00
## parent_educmaster's degree:lunch_typestandard -3.498e+00 3.411e+00
## parent_educsome college:lunch_typestandard -1.325e+00 1.452e+00
## parent_educsome high school:lunch_typestandard -1.557e-01 1.511e+00
## parent_educbachelor's degree:test_prepnone -2.759e+00 1.648e+00
## parent_educhigh school:test_prepnone 5.634e-01 1.520e+00
## parent_educmaster's degree:test_prepnone 2.793e+00 2.655e+00
## parent_educsome college:test_prepnone -1.243e+00 1.465e+00
## parent_educsome high school:test_prepnone -7.908e-02 1.433e+00
## parent_educbachelor's degree:parent_marital_statusmarried -1.309e+00 2.883e+00
## parent_educhigh school:parent_marital_statusmarried 1.847e+00 1.966e+00
## parent_educmaster's degree:parent_marital_statusmarried -6.488e+00 2.832e+00
## parent_educsome college:parent_marital_statusmarried -1.349e+00 1.863e+00
## parent_educsome high school:parent_marital_statusmarried -4.263e-01 1.899e+00
## parent_educbachelor's degree:parent_marital_statussingle 9.234e-01 3.226e+00
## parent_educhigh school:parent_marital_statussingle 1.002e+00 2.109e+00
## parent_educmaster's degree:parent_marital_statussingle -3.543e+00 2.970e+00
## parent_educsome college:parent_marital_statussingle -8.280e-01 2.027e+00
## parent_educsome high school:parent_marital_statussingle 2.050e+00 2.130e+00
## parent_educbachelor's degree:parent_marital_statuswidowed 3.893e+00 2.711e+01
## parent_educhigh school:parent_marital_statuswidowed 2.680e+01 3.071e+01
## parent_educmaster's degree:parent_marital_statuswidowed 1.524e+01 1.702e+01
## parent_educsome college:parent_marital_statuswidowed 3.226e+01 2.081e+01
## parent_educsome high school:parent_marital_statuswidowed 3.090e+01 2.434e+01
## parent_educbachelor's degree:practice_sportregularly -4.111e+00 2.830e+00
## parent_educhigh school:practice_sportregularly -3.260e+00 2.329e+00
## parent_educmaster's degree:practice_sportregularly -2.114e+00 3.343e+00
## parent_educsome college:practice_sportregularly -1.400e-01 2.364e+00
## parent_educsome high school:practice_sportregularly -1.067e+00 2.252e+00
## parent_educbachelor's degree:practice_sportsometimes -3.320e+00 2.697e+00
## parent_educhigh school:practice_sportsometimes -1.526e+00 2.238e+00
## parent_educmaster's degree:practice_sportsometimes -3.695e+00 3.068e+00
## parent_educsome college:practice_sportsometimes -1.685e+00 2.318e+00
## parent_educsome high school:practice_sportsometimes 1.748e+00 2.120e+00
## parent_educbachelor's degree:is_first_childyes -1.208e+00 1.617e+00
## parent_educhigh school:is_first_childyes -1.886e+00 1.394e+00
## parent_educmaster's degree:is_first_childyes -4.500e-02 2.641e+00
## parent_educsome college:is_first_childyes -1.884e+00 1.367e+00
## parent_educsome high school:is_first_childyes -2.437e+00 1.382e+00
## parent_educbachelor's degree:transport_meansschool_bus -7.696e-01 1.662e+00
## parent_educhigh school:transport_meansschool_bus -8.944e-01 1.320e+00
## parent_educmaster's degree:transport_meansschool_bus -3.307e+00 2.095e+00
## parent_educsome college:transport_meansschool_bus 1.144e+00 1.326e+00
## parent_educsome high school:transport_meansschool_bus -1.192e+00 1.412e+00
## parent_educbachelor's degree:wkly_study_hours> 10 2.640e+00 2.425e+00
## parent_educhigh school:wkly_study_hours> 10 1.254e-01 1.987e+00
## parent_educmaster's degree:wkly_study_hours> 10 -3.371e+00 4.819e+00
## parent_educsome college:wkly_study_hours> 10 2.836e+00 2.036e+00
## parent_educsome high school:wkly_study_hours> 10 2.006e+00 2.071e+00
## parent_educbachelor's degree:wkly_study_hours10-May 1.472e+00 1.683e+00
## parent_educhigh school:wkly_study_hours10-May -2.399e-01 1.564e+00
## parent_educmaster's degree:wkly_study_hours10-May -6.587e-02 2.515e+00
## parent_educsome college:wkly_study_hours10-May 2.528e+00 1.612e+00
## parent_educsome high school:wkly_study_hours10-May 1.773e-01 1.687e+00
## parent_educbachelor's degree:writing_score -2.361e-01 1.487e-01
## parent_educhigh school:writing_score 3.596e-02 1.308e-01
## parent_educmaster's degree:writing_score -3.876e-01 2.307e-01
## parent_educsome college:writing_score -2.102e-02 1.272e-01
## parent_educsome high school:writing_score -2.740e-02 1.325e-01
## parent_educbachelor's degree:math_score 2.630e-01 1.379e-01
## parent_educhigh school:math_score 3.693e-02 1.198e-01
## parent_educmaster's degree:math_score 4.687e-01 2.429e-01
## parent_educsome college:math_score -8.838e-03 1.200e-01
## parent_educsome high school:math_score 5.598e-02 1.257e-01
## lunch_typestandard:test_prepnone -1.405e+00 1.127e+00
## lunch_typestandard:parent_marital_statusmarried -4.861e-01 1.424e+00
## lunch_typestandard:parent_marital_statussingle 1.333e+00 1.657e+00
## lunch_typestandard:parent_marital_statuswidowed 1.830e+01 2.465e+01
## lunch_typestandard:practice_sportregularly -1.667e+00 1.737e+00
## lunch_typestandard:practice_sportsometimes -6.638e-01 1.662e+00
## lunch_typestandard:is_first_childyes -4.227e-01 1.075e+00
## lunch_typestandard:transport_meansschool_bus -4.599e-01 1.023e+00
## lunch_typestandard:wkly_study_hours> 10 9.849e-01 1.564e+00
## lunch_typestandard:wkly_study_hours10-May -8.966e-01 1.202e+00
## lunch_typestandard:writing_score -1.598e-01 8.786e-02
## lunch_typestandard:math_score 1.083e-01 8.037e-02
## test_prepnone:parent_marital_statusmarried 1.929e+00 1.423e+00
## test_prepnone:parent_marital_statussingle 1.207e+00 1.643e+00
## test_prepnone:parent_marital_statuswidowed 2.444e+01 1.407e+01
## test_prepnone:practice_sportregularly 2.596e+00 1.862e+00
## test_prepnone:practice_sportsometimes 1.233e+00 1.859e+00
## test_prepnone:is_first_childyes 1.400e+00 1.062e+00
## test_prepnone:transport_meansschool_bus -1.152e+00 9.935e-01
## test_prepnone:wkly_study_hours> 10 -1.361e+00 1.562e+00
## test_prepnone:wkly_study_hours10-May -1.755e+00 1.233e+00
## test_prepnone:writing_score -6.370e-03 9.285e-02
## test_prepnone:math_score 9.062e-03 8.595e-02
## parent_marital_statusmarried:practice_sportregularly -1.226e+00 2.083e+00
## parent_marital_statussingle:practice_sportregularly -1.178e+00 2.830e+00
## parent_marital_statuswidowed:practice_sportregularly -1.507e+01 2.606e+01
## parent_marital_statusmarried:practice_sportsometimes -1.300e+00 2.046e+00
## parent_marital_statussingle:practice_sportsometimes -3.030e-01 2.765e+00
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -2.096e+00 1.588e+00
## parent_marital_statussingle:is_first_childyes -1.219e+00 1.728e+00
## parent_marital_statuswidowed:is_first_childyes -1.659e+01 9.822e+00
## parent_marital_statusmarried:transport_meansschool_bus 5.063e-01 1.284e+00
## parent_marital_statussingle:transport_meansschool_bus -5.592e-01 1.509e+00
## parent_marital_statuswidowed:transport_meansschool_bus 1.199e+01 6.336e+00
## parent_marital_statusmarried:wkly_study_hours> 10 2.837e+00 2.081e+00
## parent_marital_statussingle:wkly_study_hours> 10 3.864e+00 2.310e+00
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May -1.074e+00 1.441e+00
## parent_marital_statussingle:wkly_study_hours10-May -2.357e+00 1.615e+00
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 1.329e-01 1.210e-01
## parent_marital_statussingle:writing_score 1.592e-02 1.356e-01
## parent_marital_statuswidowed:writing_score NA NA
## parent_marital_statusmarried:math_score -7.963e-02 1.163e-01
## parent_marital_statussingle:math_score -1.076e-02 1.293e-01
## parent_marital_statuswidowed:math_score NA NA
## practice_sportregularly:is_first_childyes 2.602e+00 1.873e+00
## practice_sportsometimes:is_first_childyes 1.474e+00 1.820e+00
## practice_sportregularly:transport_meansschool_bus -1.672e+00 1.591e+00
## practice_sportsometimes:transport_meansschool_bus -1.272e+00 1.542e+00
## practice_sportregularly:wkly_study_hours> 10 -1.024e+00 2.207e+00
## practice_sportsometimes:wkly_study_hours> 10 4.400e-01 2.182e+00
## practice_sportregularly:wkly_study_hours10-May 1.784e-01 1.692e+00
## practice_sportsometimes:wkly_study_hours10-May 2.696e-02 1.683e+00
## practice_sportregularly:writing_score 2.752e-01 1.619e-01
## practice_sportsometimes:writing_score 2.861e-01 1.615e-01
## practice_sportregularly:math_score -2.517e-01 1.539e-01
## practice_sportsometimes:math_score -3.013e-01 1.503e-01
## is_first_childyes:transport_meansschool_bus 1.054e+00 9.774e-01
## is_first_childyes:wkly_study_hours> 10 -1.518e+00 1.434e+00
## is_first_childyes:wkly_study_hours10-May -8.117e-01 1.089e+00
## is_first_childyes:writing_score -3.956e-02 8.887e-02
## is_first_childyes:math_score 6.301e-02 8.572e-02
## transport_meansschool_bus:wkly_study_hours> 10 -7.879e-01 1.381e+00
## transport_meansschool_bus:wkly_study_hours10-May 8.323e-01 9.872e-01
## transport_meansschool_bus:writing_score -5.895e-02 8.555e-02
## transport_meansschool_bus:math_score -8.323e-04 7.997e-02
## wkly_study_hours> 10:writing_score -2.377e-01 1.372e-01
## wkly_study_hours10-May:writing_score -1.762e-01 9.345e-02
## wkly_study_hours> 10:math_score 2.307e-01 1.285e-01
## wkly_study_hours10-May:math_score 1.730e-01 9.378e-02
## writing_score:math_score 1.096e-03 1.002e-03
## t value Pr(>|t|)
## (Intercept) -0.408 0.683671
## gendermale 0.268 0.789175
## ethnic_groupgroup B 1.064 0.288209
## ethnic_groupgroup C 1.058 0.290906
## ethnic_groupgroup D 0.665 0.506628
## ethnic_groupgroup E -0.396 0.692529
## parent_educbachelor's degree 0.605 0.545774
## parent_educhigh school -0.333 0.738971
## parent_educmaster's degree -0.418 0.676188
## parent_educsome college 0.259 0.795820
## parent_educsome high school -0.577 0.564153
## lunch_typestandard 0.640 0.522836
## test_prepnone 0.189 0.850066
## parent_marital_statusmarried -1.155 0.248940
## parent_marital_statussingle -1.041 0.298642
## parent_marital_statuswidowed -0.838 0.402697
## practice_sportregularly -0.357 0.721210
## practice_sportsometimes -0.058 0.953423
## is_first_childyes 0.586 0.558477
## transport_meansschool_bus 1.580 0.115044
## wkly_study_hours> 10 0.532 0.594786
## wkly_study_hours10-May 1.365 0.173265
## writing_score 3.421 0.000700 ***
## math_score 0.068 0.945767
## gendermale:ethnic_groupgroup B 0.099 0.921492
## gendermale:ethnic_groupgroup C 0.822 0.411883
## gendermale:ethnic_groupgroup D 0.460 0.645891
## gendermale:ethnic_groupgroup E 0.605 0.545254
## gendermale:parent_educbachelor's degree -1.203 0.229964
## gendermale:parent_educhigh school -0.293 0.770029
## gendermale:parent_educmaster's degree -2.338 0.019975 *
## gendermale:parent_educsome college -0.154 0.877599
## gendermale:parent_educsome high school 0.017 0.986472
## gendermale:lunch_typestandard -1.325 0.185974
## gendermale:test_prepnone -0.319 0.750210
## gendermale:parent_marital_statusmarried 1.018 0.309505
## gendermale:parent_marital_statussingle -0.161 0.871811
## gendermale:parent_marital_statuswidowed 0.182 0.856025
## gendermale:practice_sportregularly 1.106 0.269415
## gendermale:practice_sportsometimes 1.528 0.127446
## gendermale:is_first_childyes -0.172 0.863917
## gendermale:transport_meansschool_bus -0.192 0.847681
## gendermale:wkly_study_hours> 10 -1.695 0.091062 .
## gendermale:wkly_study_hours10-May -0.946 0.345031
## gendermale:writing_score -1.446 0.149044
## gendermale:math_score 1.158 0.247589
## ethnic_groupgroup B:parent_educbachelor's degree 0.236 0.813286
## ethnic_groupgroup C:parent_educbachelor's degree 0.542 0.588126
## ethnic_groupgroup D:parent_educbachelor's degree 0.457 0.648281
## ethnic_groupgroup E:parent_educbachelor's degree -0.276 0.782536
## ethnic_groupgroup B:parent_educhigh school -0.395 0.693296
## ethnic_groupgroup C:parent_educhigh school 0.311 0.755742
## ethnic_groupgroup D:parent_educhigh school -0.192 0.848179
## ethnic_groupgroup E:parent_educhigh school 0.531 0.595735
## ethnic_groupgroup B:parent_educmaster's degree 3.291 0.001103 **
## ethnic_groupgroup C:parent_educmaster's degree 3.131 0.001896 **
## ethnic_groupgroup D:parent_educmaster's degree 2.735 0.006573 **
## ethnic_groupgroup E:parent_educmaster's degree 2.310 0.021476 *
## ethnic_groupgroup B:parent_educsome college 0.179 0.858399
## ethnic_groupgroup C:parent_educsome college 0.590 0.555417
## ethnic_groupgroup D:parent_educsome college 0.765 0.444938
## ethnic_groupgroup E:parent_educsome college 2.135 0.033479 *
## ethnic_groupgroup B:parent_educsome high school 1.361 0.174402
## ethnic_groupgroup C:parent_educsome high school 1.452 0.147562
## ethnic_groupgroup D:parent_educsome high school 0.829 0.407523
## ethnic_groupgroup E:parent_educsome high school 2.754 0.006213 **
## ethnic_groupgroup B:lunch_typestandard 1.961 0.050678 .
## ethnic_groupgroup C:lunch_typestandard 2.437 0.015326 *
## ethnic_groupgroup D:lunch_typestandard 3.694 0.000258 ***
## ethnic_groupgroup E:lunch_typestandard 1.010 0.313025
## ethnic_groupgroup B:test_prepnone -0.194 0.846211
## ethnic_groupgroup C:test_prepnone 0.774 0.439756
## ethnic_groupgroup D:test_prepnone 0.261 0.794567
## ethnic_groupgroup E:test_prepnone 0.836 0.403997
## ethnic_groupgroup B:parent_marital_statusmarried 2.532 0.011802 *
## ethnic_groupgroup C:parent_marital_statusmarried 1.240 0.215834
## ethnic_groupgroup D:parent_marital_statusmarried 0.654 0.513483
## ethnic_groupgroup E:parent_marital_statusmarried 1.374 0.170193
## ethnic_groupgroup B:parent_marital_statussingle 2.856 0.004553 **
## ethnic_groupgroup C:parent_marital_statussingle 2.081 0.038193 *
## ethnic_groupgroup D:parent_marital_statussingle 2.032 0.042887 *
## ethnic_groupgroup E:parent_marital_statussingle 3.309 0.001038 **
## ethnic_groupgroup B:parent_marital_statuswidowed -1.059 0.290487
## ethnic_groupgroup C:parent_marital_statuswidowed -1.547 0.122696
## ethnic_groupgroup D:parent_marital_statuswidowed -0.666 0.505847
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly -0.650 0.516300
## ethnic_groupgroup C:practice_sportregularly -0.950 0.342711
## ethnic_groupgroup D:practice_sportregularly -0.661 0.508816
## ethnic_groupgroup E:practice_sportregularly 0.496 0.620400
## ethnic_groupgroup B:practice_sportsometimes -0.110 0.912833
## ethnic_groupgroup C:practice_sportsometimes -0.402 0.687998
## ethnic_groupgroup D:practice_sportsometimes -0.431 0.666704
## ethnic_groupgroup E:practice_sportsometimes 0.418 0.676110
## ethnic_groupgroup B:is_first_childyes -1.128 0.260168
## ethnic_groupgroup C:is_first_childyes -1.560 0.119672
## ethnic_groupgroup D:is_first_childyes -1.585 0.113826
## ethnic_groupgroup E:is_first_childyes -1.736 0.083387 .
## ethnic_groupgroup B:transport_meansschool_bus -0.869 0.385641
## ethnic_groupgroup C:transport_meansschool_bus -0.515 0.607133
## ethnic_groupgroup D:transport_meansschool_bus 0.850 0.395728
## ethnic_groupgroup E:transport_meansschool_bus 0.330 0.741479
## ethnic_groupgroup B:wkly_study_hours> 10 -0.409 0.682699
## ethnic_groupgroup C:wkly_study_hours> 10 -0.515 0.606873
## ethnic_groupgroup D:wkly_study_hours> 10 -1.389 0.165797
## ethnic_groupgroup E:wkly_study_hours> 10 -0.920 0.358113
## ethnic_groupgroup B:wkly_study_hours10-May -0.255 0.798687
## ethnic_groupgroup C:wkly_study_hours10-May -1.234 0.218172
## ethnic_groupgroup D:wkly_study_hours10-May -1.297 0.195535
## ethnic_groupgroup E:wkly_study_hours10-May -1.885 0.060300 .
## ethnic_groupgroup B:writing_score -1.060 0.289896
## ethnic_groupgroup C:writing_score -0.260 0.794873
## ethnic_groupgroup D:writing_score -0.514 0.607454
## ethnic_groupgroup E:writing_score -0.139 0.889829
## ethnic_groupgroup B:math_score -0.109 0.913438
## ethnic_groupgroup C:math_score -0.810 0.418506
## ethnic_groupgroup D:math_score -0.460 0.645611
## ethnic_groupgroup E:math_score -0.318 0.750960
## parent_educbachelor's degree:lunch_typestandard -0.336 0.736915
## parent_educhigh school:lunch_typestandard -0.426 0.670128
## parent_educmaster's degree:lunch_typestandard -1.025 0.305876
## parent_educsome college:lunch_typestandard -0.912 0.362201
## parent_educsome high school:lunch_typestandard -0.103 0.917960
## parent_educbachelor's degree:test_prepnone -1.674 0.095108 .
## parent_educhigh school:test_prepnone 0.371 0.711100
## parent_educmaster's degree:test_prepnone 1.052 0.293532
## parent_educsome college:test_prepnone -0.849 0.396664
## parent_educsome high school:test_prepnone -0.055 0.956034
## parent_educbachelor's degree:parent_marital_statusmarried -0.454 0.650059
## parent_educhigh school:parent_marital_statusmarried 0.939 0.348155
## parent_educmaster's degree:parent_marital_statusmarried -2.290 0.022604 *
## parent_educsome college:parent_marital_statusmarried -0.724 0.469449
## parent_educsome high school:parent_marital_statusmarried -0.225 0.822483
## parent_educbachelor's degree:parent_marital_statussingle 0.286 0.774886
## parent_educhigh school:parent_marital_statussingle 0.475 0.635097
## parent_educmaster's degree:parent_marital_statussingle -1.193 0.233806
## parent_educsome college:parent_marital_statussingle -0.408 0.683176
## parent_educsome high school:parent_marital_statussingle 0.962 0.336653
## parent_educbachelor's degree:parent_marital_statuswidowed 0.144 0.885883
## parent_educhigh school:parent_marital_statuswidowed 0.873 0.383467
## parent_educmaster's degree:parent_marital_statuswidowed 0.896 0.371104
## parent_educsome college:parent_marital_statuswidowed 1.550 0.122008
## parent_educsome high school:parent_marital_statuswidowed 1.269 0.205167
## parent_educbachelor's degree:practice_sportregularly -1.453 0.147210
## parent_educhigh school:practice_sportregularly -1.399 0.162620
## parent_educmaster's degree:practice_sportregularly -0.632 0.527626
## parent_educsome college:practice_sportregularly -0.059 0.952808
## parent_educsome high school:practice_sportregularly -0.474 0.635856
## parent_educbachelor's degree:practice_sportsometimes -1.231 0.219177
## parent_educhigh school:practice_sportsometimes -0.682 0.495762
## parent_educmaster's degree:practice_sportsometimes -1.204 0.229249
## parent_educsome college:practice_sportsometimes -0.727 0.467769
## parent_educsome high school:practice_sportsometimes 0.824 0.410372
## parent_educbachelor's degree:is_first_childyes -0.747 0.455633
## parent_educhigh school:is_first_childyes -1.353 0.176995
## parent_educmaster's degree:is_first_childyes -0.017 0.986418
## parent_educsome college:is_first_childyes -1.379 0.168938
## parent_educsome high school:is_first_childyes -1.763 0.078783 .
## parent_educbachelor's degree:transport_meansschool_bus -0.463 0.643567
## parent_educhigh school:transport_meansschool_bus -0.677 0.498582
## parent_educmaster's degree:transport_meansschool_bus -1.578 0.115479
## parent_educsome college:transport_meansschool_bus 0.863 0.388977
## parent_educsome high school:transport_meansschool_bus -0.844 0.399205
## parent_educbachelor's degree:wkly_study_hours> 10 1.089 0.277050
## parent_educhigh school:wkly_study_hours> 10 0.063 0.949727
## parent_educmaster's degree:wkly_study_hours> 10 -0.699 0.484758
## parent_educsome college:wkly_study_hours> 10 1.393 0.164477
## parent_educsome high school:wkly_study_hours> 10 0.969 0.333468
## parent_educbachelor's degree:wkly_study_hours10-May 0.875 0.382218
## parent_educhigh school:wkly_study_hours10-May -0.153 0.878185
## parent_educmaster's degree:wkly_study_hours10-May -0.026 0.979122
## parent_educsome college:wkly_study_hours10-May 1.569 0.117603
## parent_educsome high school:wkly_study_hours10-May 0.105 0.916353
## parent_educbachelor's degree:writing_score -1.587 0.113408
## parent_educhigh school:writing_score 0.275 0.783591
## parent_educmaster's degree:writing_score -1.680 0.093863 .
## parent_educsome college:writing_score -0.165 0.868787
## parent_educsome high school:writing_score -0.207 0.836274
## parent_educbachelor's degree:math_score 1.908 0.057252 .
## parent_educhigh school:math_score 0.308 0.758001
## parent_educmaster's degree:math_score 1.930 0.054439 .
## parent_educsome college:math_score -0.074 0.941319
## parent_educsome high school:math_score 0.445 0.656248
## lunch_typestandard:test_prepnone -1.246 0.213597
## lunch_typestandard:parent_marital_statusmarried -0.341 0.733035
## lunch_typestandard:parent_marital_statussingle 0.804 0.421713
## lunch_typestandard:parent_marital_statuswidowed 0.743 0.458152
## lunch_typestandard:practice_sportregularly -0.960 0.337845
## lunch_typestandard:practice_sportsometimes -0.400 0.689756
## lunch_typestandard:is_first_childyes -0.393 0.694445
## lunch_typestandard:transport_meansschool_bus -0.450 0.653202
## lunch_typestandard:wkly_study_hours> 10 0.630 0.529257
## lunch_typestandard:wkly_study_hours10-May -0.746 0.456417
## lunch_typestandard:writing_score -1.819 0.069813 .
## lunch_typestandard:math_score 1.348 0.178568
## test_prepnone:parent_marital_statusmarried 1.356 0.176095
## test_prepnone:parent_marital_statussingle 0.735 0.463029
## test_prepnone:parent_marital_statuswidowed 1.737 0.083287 .
## test_prepnone:practice_sportregularly 1.395 0.164053
## test_prepnone:practice_sportsometimes 0.663 0.507614
## test_prepnone:is_first_childyes 1.319 0.188184
## test_prepnone:transport_meansschool_bus -1.160 0.246966
## test_prepnone:wkly_study_hours> 10 -0.871 0.384281
## test_prepnone:wkly_study_hours10-May -1.424 0.155352
## test_prepnone:writing_score -0.069 0.945344
## test_prepnone:math_score 0.105 0.916095
## parent_marital_statusmarried:practice_sportregularly -0.589 0.556528
## parent_marital_statussingle:practice_sportregularly -0.416 0.677513
## parent_marital_statuswidowed:practice_sportregularly -0.578 0.563533
## parent_marital_statusmarried:practice_sportsometimes -0.635 0.525694
## parent_marital_statussingle:practice_sportsometimes -0.110 0.912789
## parent_marital_statuswidowed:practice_sportsometimes NA NA
## parent_marital_statusmarried:is_first_childyes -1.320 0.187858
## parent_marital_statussingle:is_first_childyes -0.706 0.480761
## parent_marital_statuswidowed:is_first_childyes -1.689 0.092194 .
## parent_marital_statusmarried:transport_meansschool_bus 0.394 0.693668
## parent_marital_statussingle:transport_meansschool_bus -0.371 0.711222
## parent_marital_statuswidowed:transport_meansschool_bus 1.893 0.059273 .
## parent_marital_statusmarried:wkly_study_hours> 10 1.364 0.173575
## parent_marital_statussingle:wkly_study_hours> 10 1.673 0.095263 .
## parent_marital_statuswidowed:wkly_study_hours> 10 NA NA
## parent_marital_statusmarried:wkly_study_hours10-May -0.745 0.456721
## parent_marital_statussingle:wkly_study_hours10-May -1.460 0.145295
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 1.098 0.272979
## parent_marital_statussingle:writing_score 0.117 0.906626
## parent_marital_statuswidowed:writing_score NA NA
## parent_marital_statusmarried:math_score -0.685 0.493846
## parent_marital_statussingle:math_score -0.083 0.933740
## parent_marital_statuswidowed:math_score NA NA
## practice_sportregularly:is_first_childyes 1.389 0.165673
## practice_sportsometimes:is_first_childyes 0.810 0.418475
## practice_sportregularly:transport_meansschool_bus -1.051 0.294033
## practice_sportsometimes:transport_meansschool_bus -0.825 0.409953
## practice_sportregularly:wkly_study_hours> 10 -0.464 0.642960
## practice_sportsometimes:wkly_study_hours> 10 0.202 0.840284
## practice_sportregularly:wkly_study_hours10-May 0.105 0.916088
## practice_sportsometimes:wkly_study_hours10-May 0.016 0.987230
## practice_sportregularly:writing_score 1.700 0.090064 .
## practice_sportsometimes:writing_score 1.772 0.077311 .
## practice_sportregularly:math_score -1.635 0.102909
## practice_sportsometimes:math_score -2.005 0.045740 *
## is_first_childyes:transport_meansschool_bus 1.078 0.281579
## is_first_childyes:wkly_study_hours> 10 -1.059 0.290334
## is_first_childyes:wkly_study_hours10-May -0.746 0.456423
## is_first_childyes:writing_score -0.445 0.656475
## is_first_childyes:math_score 0.735 0.462815
## transport_meansschool_bus:wkly_study_hours> 10 -0.571 0.568631
## transport_meansschool_bus:wkly_study_hours10-May 0.843 0.399765
## transport_meansschool_bus:writing_score -0.689 0.491249
## transport_meansschool_bus:math_score -0.010 0.991702
## wkly_study_hours> 10:writing_score -1.733 0.084006 .
## wkly_study_hours10-May:writing_score -1.886 0.060213 .
## wkly_study_hours> 10:math_score 1.795 0.073500 .
## wkly_study_hours10-May:math_score 1.844 0.066012 .
## writing_score:math_score 1.094 0.274947
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.886 on 340 degrees of freedom
## Multiple R-squared: 0.962, Adjusted R-squared: 0.9342
## F-statistic: 34.57 on 249 and 340 DF, p-value: < 2.2e-16stepwise_model_read2 <- step(full_fit_read2, direction = "both", trace = 1)## Start: AIC=1776.62
## reading_score ~ (gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score)^2
##
## Df Sum of Sq RSS AIC
## - parent_educ:wkly_study_hours 10 99.04 5234.3 1767.9
## - parent_educ:lunch_type 5 25.60 5160.8 1769.5
## - ethnic_group:math_score 4 18.16 5153.4 1770.7
## - parent_marital_status:practice_sport 4 19.43 5154.7 1770.8
## - gender:ethnic_group 4 19.67 5154.9 1770.9
## - practice_sport:wkly_study_hours 4 25.16 5160.4 1771.5
## - ethnic_group:practice_sport 8 97.36 5232.6 1771.7
## - ethnic_group:writing_score 4 27.67 5162.9 1771.8
## - parent_educ:is_first_child 5 59.40 5194.7 1773.4
## - parent_marital_status:math_score 2 12.48 5147.7 1774.0
## - ethnic_group:test_prep 4 47.58 5182.8 1774.1
## - parent_marital_status:transport_means 2 14.64 5149.9 1774.3
## - practice_sport:transport_means 2 16.71 5152.0 1774.5
## - ethnic_group:is_first_child 4 52.34 5187.6 1774.6
## - transport_means:math_score 1 0.00 5135.3 1774.6
## - test_prep:writing_score 1 0.07 5135.3 1774.6
## - test_prep:math_score 1 0.17 5135.4 1774.6
## - is_first_child:wkly_study_hours 2 17.71 5153.0 1774.7
## - gender:is_first_child 1 0.44 5135.7 1774.7
## - gender:transport_means 1 0.56 5135.8 1774.7
## - gender:test_prep 1 1.53 5136.8 1774.8
## - lunch_type:practice_sport 2 19.36 5154.6 1774.8
## - lunch_type:is_first_child 1 2.33 5137.6 1774.9
## - is_first_child:writing_score 1 2.99 5138.2 1775.0
## - lunch_type:transport_means 1 3.05 5138.3 1775.0
## - transport_means:writing_score 1 7.17 5142.4 1775.4
## - is_first_child:math_score 1 8.16 5143.4 1775.6
## - transport_means:wkly_study_hours 2 29.96 5165.2 1776.0
## - test_prep:parent_marital_status 2 30.23 5165.5 1776.1
## - test_prep:wkly_study_hours 2 30.65 5165.9 1776.1
## - parent_marital_status:is_first_child 2 30.66 5165.9 1776.1
## - parent_marital_status:writing_score 2 31.63 5166.9 1776.2
## - lunch_type:wkly_study_hours 2 31.64 5166.9 1776.2
## <none> 5135.2 1776.6
## - is_first_child:transport_means 1 17.57 5152.8 1776.6
## - writing_score:math_score 1 18.06 5153.3 1776.7
## - gender:practice_sport 2 36.55 5171.8 1776.8
## - lunch_type:parent_marital_status 2 37.01 5172.3 1776.9
## - gender:math_score 1 20.26 5155.5 1776.9
## - test_prep:transport_means 1 20.31 5155.6 1777.0
## - practice_sport:is_first_child 2 39.42 5174.7 1777.1
## - lunch_type:test_prep 1 23.45 5158.7 1777.3
## - parent_educ:writing_score 5 94.58 5229.8 1777.4
## - parent_educ:transport_means 5 94.90 5230.1 1777.4
## - gender:wkly_study_hours 2 43.49 5178.7 1777.6
## - test_prep:is_first_child 1 26.26 5161.5 1777.6
## - gender:lunch_type 1 26.53 5161.8 1777.7
## - gender:parent_marital_status 2 44.65 5179.9 1777.7
## - lunch_type:math_score 1 27.44 5162.7 1777.8
## - test_prep:practice_sport 2 45.43 5180.7 1777.8
## - parent_educ:test_prep 5 98.73 5234.0 1777.8
## - gender:writing_score 1 31.59 5166.8 1778.2
## - practice_sport:writing_score 2 49.70 5185.0 1778.3
## - gender:parent_educ 5 105.13 5240.4 1778.6
## - practice_sport:math_score 2 60.80 5196.1 1779.6
## - wkly_study_hours:math_score 2 65.25 5200.5 1780.1
## - wkly_study_hours:writing_score 2 67.41 5202.7 1780.3
## - lunch_type:writing_score 1 49.97 5185.2 1780.3
## - parent_educ:math_score 5 121.69 5256.9 1780.4
## - ethnic_group:transport_means 4 109.59 5244.8 1781.1
## - parent_educ:parent_marital_status 11 235.69 5370.9 1781.1
## - ethnic_group:wkly_study_hours 8 199.07 5334.3 1783.1
## - parent_educ:practice_sport 10 235.54 5370.8 1783.1
## - parent_marital_status:wkly_study_hours 4 154.17 5289.4 1786.1
## - ethnic_group:parent_educ 20 524.88 5660.1 1794.0
## - ethnic_group:lunch_type 4 244.78 5380.0 1796.1
## - ethnic_group:parent_marital_status 8 321.58 5456.8 1796.5
##
## Step: AIC=1767.89
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + ethnic_group:math_score + parent_educ:lunch_type +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:math_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:lunch_type 5 32.14 5266.4 1761.5
## - ethnic_group:math_score 4 18.61 5252.9 1762.0
## - ethnic_group:writing_score 4 21.90 5256.2 1762.3
## - parent_marital_status:practice_sport 4 23.11 5257.4 1762.5
## - gender:ethnic_group 4 24.33 5258.6 1762.6
## - practice_sport:wkly_study_hours 4 37.01 5271.3 1764.0
## - ethnic_group:practice_sport 8 113.81 5348.1 1764.6
## - ethnic_group:is_first_child 4 42.08 5276.4 1764.6
## - parent_marital_status:math_score 2 13.13 5247.4 1765.4
## - is_first_child:wkly_study_hours 2 14.26 5248.5 1765.5
## - parent_marital_status:transport_means 2 14.69 5249.0 1765.5
## - practice_sport:transport_means 2 16.02 5250.3 1765.7
## - lunch_type:practice_sport 2 16.65 5250.9 1765.8
## - parent_educ:is_first_child 5 70.86 5305.2 1765.8
## - gender:is_first_child 1 0.03 5234.3 1765.9
## - test_prep:math_score 1 0.04 5234.3 1765.9
## - test_prep:writing_score 1 0.13 5234.4 1765.9
## - transport_means:math_score 1 0.59 5234.9 1766.0
## - gender:test_prep 1 0.99 5235.3 1766.0
## - lunch_type:is_first_child 1 1.11 5235.4 1766.0
## - gender:transport_means 1 2.02 5236.3 1766.1
## - lunch_type:transport_means 1 3.77 5238.1 1766.3
## - is_first_child:writing_score 1 4.08 5238.4 1766.3
## - ethnic_group:test_prep 4 60.96 5295.2 1766.7
## - is_first_child:math_score 1 9.38 5243.7 1767.0
## - parent_marital_status:writing_score 2 31.56 5265.8 1767.4
## - parent_educ:writing_score 5 85.74 5320.0 1767.5
## - writing_score:math_score 1 14.35 5248.6 1767.5
## - is_first_child:transport_means 1 14.50 5248.8 1767.5
## - parent_marital_status:is_first_child 2 32.50 5266.8 1767.5
## - transport_means:writing_score 1 14.93 5249.2 1767.6
## - test_prep:wkly_study_hours 2 33.96 5268.2 1767.7
## - lunch_type:test_prep 1 16.60 5250.9 1767.8
## - test_prep:is_first_child 1 16.92 5251.2 1767.8
## - parent_educ:transport_means 5 89.08 5323.4 1767.8
## - test_prep:parent_marital_status 2 35.26 5269.6 1767.8
## <none> 5234.3 1767.9
## - transport_means:wkly_study_hours 2 35.66 5270.0 1767.9
## - lunch_type:parent_marital_status 2 36.82 5271.1 1768.0
## - practice_sport:is_first_child 2 39.13 5273.4 1768.3
## - gender:math_score 1 23.03 5257.3 1768.5
## - lunch_type:math_score 1 24.34 5258.6 1768.6
## - gender:parent_marital_status 2 42.49 5276.8 1768.7
## - gender:lunch_type 1 24.76 5259.0 1768.7
## - test_prep:practice_sport 2 43.27 5277.6 1768.8
## - test_prep:transport_means 1 26.63 5260.9 1768.9
## - gender:parent_educ 5 103.22 5337.5 1769.4
## - gender:writing_score 1 33.17 5267.5 1769.6
## - gender:practice_sport 2 53.46 5287.8 1769.9
## - parent_educ:math_score 5 108.90 5343.2 1770.0
## - gender:wkly_study_hours 2 58.51 5292.8 1770.5
## - practice_sport:writing_score 2 60.14 5294.4 1770.6
## - ethnic_group:transport_means 4 97.19 5331.5 1770.7
## - lunch_type:writing_score 1 43.30 5277.6 1770.8
## - lunch_type:wkly_study_hours 2 62.65 5296.9 1770.9
## - ethnic_group:wkly_study_hours 8 177.77 5412.1 1771.6
## - wkly_study_hours:math_score 2 72.48 5306.8 1772.0
## - parent_educ:parent_marital_status 11 238.98 5473.3 1772.2
## - wkly_study_hours:writing_score 2 77.99 5312.3 1772.6
## - practice_sport:math_score 2 80.83 5315.1 1772.9
## - parent_educ:practice_sport 10 231.64 5465.9 1773.4
## - parent_educ:test_prep 5 142.86 5377.2 1773.8
## + parent_educ:wkly_study_hours 10 99.04 5135.2 1776.6
## - parent_marital_status:wkly_study_hours 4 160.99 5395.3 1777.8
## - ethnic_group:parent_educ 20 533.53 5767.8 1785.2
## - ethnic_group:lunch_type 4 231.80 5466.1 1785.5
## - ethnic_group:parent_marital_status 8 310.43 5544.7 1785.9
##
## Step: AIC=1761.5
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + ethnic_group:math_score + parent_educ:test_prep +
## parent_educ:parent_marital_status + parent_educ:practice_sport +
## parent_educ:is_first_child + parent_educ:transport_means +
## parent_educ:writing_score + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:math_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:math_score 4 23.66 5290.1 1756.2
## - gender:ethnic_group 4 25.16 5291.6 1756.3
## - ethnic_group:writing_score 4 25.95 5292.4 1756.4
## - parent_marital_status:practice_sport 4 25.97 5292.4 1756.4
## - practice_sport:wkly_study_hours 4 31.79 5298.2 1757.0
## - ethnic_group:is_first_child 4 39.67 5306.1 1757.9
## - parent_marital_status:math_score 2 8.91 5275.3 1758.5
## - parent_marital_status:transport_means 2 10.76 5277.2 1758.7
## - ethnic_group:practice_sport 8 120.14 5386.6 1758.8
## - is_first_child:wkly_study_hours 2 13.18 5279.6 1759.0
## - practice_sport:transport_means 2 15.73 5282.2 1759.3
## - parent_educ:is_first_child 5 71.51 5337.9 1759.5
## - gender:is_first_child 1 0.00 5266.4 1759.5
## - test_prep:writing_score 1 0.04 5266.5 1759.5
## - transport_means:math_score 1 0.29 5266.7 1759.5
## - test_prep:math_score 1 0.33 5266.8 1759.5
## - lunch_type:is_first_child 1 1.81 5268.2 1759.7
## - lunch_type:transport_means 1 2.05 5268.5 1759.7
## - gender:test_prep 1 2.06 5268.5 1759.7
## - gender:transport_means 1 2.09 5268.5 1759.7
## - lunch_type:practice_sport 2 21.40 5287.8 1759.9
## - is_first_child:writing_score 1 3.62 5270.1 1759.9
## - parent_educ:writing_score 5 78.62 5345.0 1760.2
## - parent_marital_status:writing_score 2 25.19 5291.6 1760.3
## - is_first_child:math_score 1 8.25 5274.7 1760.4
## - ethnic_group:test_prep 4 66.19 5332.6 1760.9
## - transport_means:writing_score 1 13.11 5279.5 1761.0
## - parent_educ:transport_means 5 85.44 5351.9 1761.0
## - is_first_child:transport_means 1 14.02 5280.4 1761.1
## - writing_score:math_score 1 15.93 5282.4 1761.3
## <none> 5266.4 1761.5
## - test_prep:is_first_child 1 18.16 5284.6 1761.5
## - parent_marital_status:is_first_child 2 36.16 5302.6 1761.5
## - test_prep:parent_marital_status 2 36.26 5302.7 1761.5
## - transport_means:wkly_study_hours 2 36.28 5302.7 1761.5
## - gender:parent_marital_status 2 36.95 5303.4 1761.6
## - gender:lunch_type 1 21.22 5287.6 1761.9
## - gender:math_score 1 22.00 5288.4 1762.0
## - lunch_type:test_prep 1 22.17 5288.6 1762.0
## - lunch_type:math_score 1 22.77 5289.2 1762.0
## - test_prep:wkly_study_hours 2 41.04 5307.5 1762.1
## - gender:parent_educ 5 96.27 5362.7 1762.2
## - lunch_type:parent_marital_status 2 43.24 5309.7 1762.3
## - practice_sport:is_first_child 2 45.52 5312.0 1762.6
## - test_prep:transport_means 1 28.32 5294.8 1762.7
## - test_prep:practice_sport 2 47.65 5314.1 1762.8
## - gender:writing_score 1 32.09 5298.5 1763.1
## - gender:practice_sport 2 53.88 5320.3 1763.5
## - parent_educ:math_score 5 109.55 5376.0 1763.7
## - parent_educ:parent_marital_status 11 225.10 5491.5 1764.2
## - ethnic_group:transport_means 4 96.39 5362.8 1764.2
## - practice_sport:writing_score 2 61.03 5327.5 1764.3
## - lunch_type:writing_score 1 43.24 5309.7 1764.3
## - lunch_type:wkly_study_hours 2 61.88 5328.3 1764.4
## - ethnic_group:wkly_study_hours 8 174.21 5440.6 1764.7
## - gender:wkly_study_hours 2 70.77 5337.2 1765.4
## - wkly_study_hours:math_score 2 80.04 5346.5 1766.4
## - practice_sport:math_score 2 83.53 5350.0 1766.8
## - wkly_study_hours:writing_score 2 88.59 5355.0 1767.3
## + parent_educ:lunch_type 5 32.14 5234.3 1767.9
## - parent_educ:test_prep 5 151.06 5417.5 1768.2
## - parent_educ:practice_sport 10 250.79 5517.2 1769.0
## + parent_educ:wkly_study_hours 10 105.59 5160.8 1769.5
## - parent_marital_status:wkly_study_hours 4 172.74 5439.2 1772.5
## - ethnic_group:lunch_type 4 231.69 5498.1 1778.9
## - ethnic_group:parent_educ 20 539.60 5806.0 1779.0
## - ethnic_group:parent_marital_status 8 318.72 5585.2 1780.2
##
## Step: AIC=1756.15
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:ethnic_group + gender:parent_educ + gender:lunch_type +
## gender:test_prep + gender:parent_marital_status + gender:practice_sport +
## gender:is_first_child + gender:transport_means + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:math_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:ethnic_group 4 7.59 5297.7 1749.0
## - parent_marital_status:practice_sport 4 26.65 5316.7 1751.1
## - practice_sport:wkly_study_hours 4 32.72 5322.8 1751.8
## - parent_marital_status:transport_means 2 6.89 5297.0 1752.9
## - ethnic_group:is_first_child 4 45.10 5335.2 1753.2
## - parent_marital_status:math_score 2 10.01 5300.1 1753.3
## - ethnic_group:practice_sport 8 119.75 5409.8 1753.3
## - parent_educ:writing_score 5 68.85 5358.9 1753.8
## - is_first_child:wkly_study_hours 2 14.98 5305.1 1753.8
## - practice_sport:transport_means 2 17.75 5307.8 1754.1
## - gender:is_first_child 1 0.01 5290.1 1754.2
## - test_prep:writing_score 1 0.02 5290.1 1754.2
## - test_prep:math_score 1 0.27 5290.4 1754.2
## - transport_means:math_score 1 1.09 5291.2 1754.3
## - ethnic_group:test_prep 4 55.38 5345.5 1754.3
## - parent_educ:is_first_child 5 74.08 5364.2 1754.3
## - gender:test_prep 1 1.99 5292.1 1754.4
## - lunch_type:is_first_child 1 2.31 5292.4 1754.4
## - is_first_child:writing_score 1 3.13 5293.2 1754.5
## - gender:transport_means 1 3.16 5293.3 1754.5
## - lunch_type:transport_means 1 3.51 5293.6 1754.5
## - is_first_child:math_score 1 7.55 5297.6 1755.0
## - lunch_type:practice_sport 2 26.13 5316.2 1755.0
## - parent_marital_status:writing_score 2 26.48 5316.6 1755.1
## - parent_educ:transport_means 5 84.43 5374.5 1755.5
## - gender:parent_educ 5 85.80 5375.9 1755.6
## - is_first_child:transport_means 1 14.87 5305.0 1755.8
## - writing_score:math_score 1 14.99 5305.1 1755.8
## - transport_means:writing_score 1 17.05 5307.1 1756.0
## <none> 5290.1 1756.2
## - transport_means:wkly_study_hours 2 37.02 5327.1 1756.3
## - gender:parent_marital_status 2 38.31 5328.4 1756.4
## - test_prep:parent_marital_status 2 38.33 5328.4 1756.4
## - parent_marital_status:is_first_child 2 38.74 5328.8 1756.5
## - lunch_type:test_prep 1 20.81 5310.9 1756.5
## - test_prep:is_first_child 1 21.44 5311.5 1756.5
## - test_prep:wkly_study_hours 2 39.48 5329.6 1756.5
## - gender:lunch_type 1 22.23 5312.3 1756.6
## - lunch_type:math_score 1 23.83 5313.9 1756.8
## - gender:math_score 1 25.68 5315.8 1757.0
## - lunch_type:parent_marital_status 2 45.57 5335.7 1757.2
## - test_prep:transport_means 1 28.43 5318.5 1757.3
## - parent_educ:math_score 5 102.76 5392.8 1757.5
## - test_prep:practice_sport 2 48.96 5339.1 1757.6
## - practice_sport:is_first_child 2 49.49 5339.6 1757.6
## - gender:writing_score 1 36.83 5326.9 1758.2
## - ethnic_group:transport_means 4 93.01 5383.1 1758.4
## - parent_educ:parent_marital_status 11 223.99 5514.1 1758.6
## - gender:practice_sport 2 60.84 5350.9 1758.9
## - lunch_type:writing_score 1 44.10 5334.2 1759.0
## - lunch_type:wkly_study_hours 2 64.25 5354.3 1759.3
## - practice_sport:writing_score 2 65.61 5355.7 1759.4
## - ethnic_group:wkly_study_hours 8 181.55 5471.6 1760.0
## - gender:wkly_study_hours 2 82.95 5373.0 1761.3
## + ethnic_group:math_score 4 23.66 5266.4 1761.5
## - parent_educ:test_prep 5 142.97 5433.1 1761.9
## + parent_educ:lunch_type 5 37.20 5252.9 1762.0
## - ethnic_group:writing_score 4 126.62 5416.7 1762.1
## - practice_sport:math_score 2 92.30 5382.4 1762.3
## - wkly_study_hours:math_score 2 92.57 5382.7 1762.4
## - parent_educ:practice_sport 10 249.75 5539.8 1763.4
## - wkly_study_hours:writing_score 2 101.96 5392.0 1763.4
## + parent_educ:wkly_study_hours 10 104.81 5185.3 1764.3
## - parent_marital_status:wkly_study_hours 4 178.15 5468.2 1767.7
## - ethnic_group:lunch_type 4 229.86 5519.9 1773.2
## - ethnic_group:parent_educ 20 551.40 5841.5 1774.6
## - ethnic_group:parent_marital_status 8 336.50 5626.6 1776.5
##
## Step: AIC=1748.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:practice_sport + parent_marital_status:is_first_child +
## parent_marital_status:transport_means + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + parent_marital_status:math_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:wkly_study_hours + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:practice_sport 4 25.00 5322.7 1743.8
## - practice_sport:wkly_study_hours 4 31.86 5329.5 1744.5
## - parent_marital_status:transport_means 2 7.88 5305.6 1745.9
## - ethnic_group:is_first_child 4 44.07 5341.8 1745.9
## - parent_marital_status:math_score 2 9.50 5307.2 1746.0
## - parent_educ:writing_score 5 67.83 5365.5 1746.5
## - ethnic_group:test_prep 4 50.49 5348.2 1746.6
## - ethnic_group:practice_sport 8 124.29 5422.0 1746.7
## - is_first_child:wkly_study_hours 2 16.79 5314.5 1746.9
## - gender:is_first_child 1 0.00 5297.7 1747.0
## - test_prep:writing_score 1 0.02 5297.7 1747.0
## - test_prep:math_score 1 0.15 5297.8 1747.0
## - practice_sport:transport_means 2 18.16 5315.8 1747.0
## - parent_educ:is_first_child 5 73.08 5370.8 1747.1
## - transport_means:math_score 1 1.18 5298.9 1747.1
## - gender:test_prep 1 1.40 5299.1 1747.2
## - lunch_type:is_first_child 1 2.55 5300.2 1747.3
## - is_first_child:writing_score 1 2.84 5300.5 1747.3
## - gender:transport_means 1 3.22 5300.9 1747.3
## - lunch_type:transport_means 1 3.69 5301.4 1747.4
## - parent_marital_status:writing_score 2 25.65 5323.3 1747.8
## - is_first_child:math_score 1 7.64 5305.3 1747.8
## - lunch_type:practice_sport 2 25.84 5323.5 1747.9
## - gender:parent_educ 5 86.68 5384.4 1748.6
## - is_first_child:transport_means 1 14.45 5312.1 1748.6
## - parent_educ:transport_means 5 87.85 5385.5 1748.7
## - test_prep:parent_marital_status 2 35.32 5333.0 1748.9
## - transport_means:writing_score 1 17.63 5315.3 1749.0
## - transport_means:wkly_study_hours 2 35.89 5333.6 1749.0
## <none> 5297.7 1749.0
## - gender:parent_marital_status 2 36.76 5334.4 1749.1
## - writing_score:math_score 1 18.76 5316.4 1749.1
## - lunch_type:test_prep 1 20.27 5318.0 1749.2
## - parent_marital_status:is_first_child 2 38.83 5336.5 1749.3
## - test_prep:is_first_child 1 21.36 5319.0 1749.4
## - test_prep:wkly_study_hours 2 40.98 5338.7 1749.5
## - lunch_type:math_score 1 24.20 5321.9 1749.7
## - gender:lunch_type 1 25.11 5322.8 1749.8
## - lunch_type:parent_marital_status 2 46.56 5344.2 1750.2
## - test_prep:transport_means 1 28.63 5326.3 1750.2
## - parent_educ:math_score 5 102.65 5400.3 1750.3
## - practice_sport:is_first_child 2 49.62 5347.3 1750.5
## - test_prep:practice_sport 2 51.00 5348.7 1750.6
## - gender:math_score 1 33.79 5331.5 1750.7
## - ethnic_group:transport_means 4 95.01 5392.7 1751.5
## - gender:writing_score 1 41.50 5339.2 1751.6
## - parent_educ:parent_marital_status 11 228.15 5525.8 1751.9
## - lunch_type:wkly_study_hours 2 63.39 5361.1 1752.0
## - gender:practice_sport 2 64.06 5361.7 1752.1
## - lunch_type:writing_score 1 46.23 5343.9 1752.1
## - practice_sport:writing_score 2 69.95 5367.6 1752.7
## - ethnic_group:wkly_study_hours 8 181.07 5478.8 1752.8
## - gender:wkly_study_hours 2 82.47 5380.2 1754.1
## - parent_educ:test_prep 5 139.88 5437.6 1754.4
## + parent_educ:lunch_type 5 36.07 5261.6 1755.0
## - wkly_study_hours:math_score 2 90.93 5388.6 1755.0
## - practice_sport:math_score 2 98.83 5396.5 1755.9
## - wkly_study_hours:writing_score 2 100.68 5398.4 1756.1
## + gender:ethnic_group 4 7.59 5290.1 1756.2
## + ethnic_group:math_score 4 6.09 5291.6 1756.3
## - parent_educ:practice_sport 10 252.44 5550.1 1756.5
## + parent_educ:wkly_study_hours 10 103.62 5194.1 1757.3
## - ethnic_group:writing_score 4 176.73 5474.4 1760.3
## - parent_marital_status:wkly_study_hours 4 180.09 5477.8 1760.7
## - ethnic_group:lunch_type 4 235.12 5532.8 1766.6
## - ethnic_group:parent_marital_status 8 332.53 5630.2 1768.9
## - ethnic_group:parent_educ 20 574.25 5871.9 1769.7
##
## Step: AIC=1743.77
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## parent_marital_status:math_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:wkly_study_hours +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:wkly_study_hours 4 35.95 5358.6 1739.7
## - ethnic_group:is_first_child 4 43.27 5366.0 1740.5
## - parent_marital_status:math_score 2 8.31 5331.0 1740.7
## - parent_marital_status:transport_means 2 9.38 5332.1 1740.8
## - parent_educ:writing_score 5 64.98 5387.7 1740.9
## - parent_educ:is_first_child 5 70.69 5393.4 1741.5
## - practice_sport:transport_means 2 17.40 5340.1 1741.7
## - ethnic_group:test_prep 4 54.26 5376.9 1741.8
## - test_prep:math_score 1 0.06 5322.7 1741.8
## - gender:is_first_child 1 0.13 5322.8 1741.8
## - test_prep:writing_score 1 0.13 5322.8 1741.8
## - transport_means:math_score 1 0.87 5323.6 1741.9
## - lunch_type:is_first_child 1 0.90 5323.6 1741.9
## - is_first_child:wkly_study_hours 2 19.24 5341.9 1741.9
## - gender:test_prep 1 1.54 5324.2 1741.9
## - lunch_type:transport_means 1 2.56 5325.2 1742.0
## - gender:transport_means 1 3.34 5326.0 1742.1
## - is_first_child:writing_score 1 4.19 5326.9 1742.2
## - parent_marital_status:writing_score 2 23.09 5345.8 1742.3
## - lunch_type:practice_sport 2 26.96 5349.7 1742.8
## - is_first_child:transport_means 1 10.09 5332.8 1742.9
## - is_first_child:math_score 1 10.22 5332.9 1742.9
## - parent_educ:transport_means 5 83.88 5406.6 1743.0
## - gender:parent_educ 5 85.35 5408.0 1743.2
## - ethnic_group:practice_sport 8 145.31 5468.0 1743.7
## - transport_means:wkly_study_hours 2 35.36 5358.0 1743.7
## - transport_means:writing_score 1 18.06 5340.7 1743.8
## <none> 5322.7 1743.8
## - gender:parent_marital_status 2 37.16 5359.9 1743.9
## - test_prep:is_first_child 1 19.22 5341.9 1743.9
## - test_prep:parent_marital_status 2 37.89 5360.6 1744.0
## - parent_educ:parent_marital_status 12 224.32 5547.0 1744.1
## - lunch_type:test_prep 1 21.68 5344.4 1744.2
## - parent_marital_status:is_first_child 2 40.22 5362.9 1744.2
## - writing_score:math_score 1 22.15 5344.8 1744.2
## - test_prep:wkly_study_hours 2 46.29 5369.0 1744.9
## - lunch_type:math_score 1 28.65 5351.3 1744.9
## - parent_educ:math_score 5 101.82 5424.5 1745.0
## - gender:lunch_type 1 29.83 5352.5 1745.1
## - lunch_type:parent_marital_status 2 49.87 5372.6 1745.3
## - test_prep:transport_means 1 31.76 5354.4 1745.3
## - test_prep:practice_sport 2 51.57 5374.3 1745.5
## - gender:math_score 1 36.34 5359.0 1745.8
## - practice_sport:is_first_child 2 54.59 5377.3 1745.8
## - lunch_type:wkly_study_hours 2 56.88 5379.6 1746.0
## - ethnic_group:transport_means 4 95.44 5418.1 1746.3
## - gender:practice_sport 2 62.49 5385.2 1746.7
## - gender:writing_score 1 44.93 5367.6 1746.7
## - ethnic_group:wkly_study_hours 8 178.86 5501.6 1747.3
## - practice_sport:writing_score 2 68.21 5390.9 1747.3
## - lunch_type:writing_score 1 56.03 5378.7 1748.0
## - parent_educ:test_prep 5 136.96 5459.6 1748.8
## - gender:wkly_study_hours 2 83.19 5405.9 1748.9
## + parent_marital_status:practice_sport 4 25.00 5297.7 1749.0
## + parent_educ:lunch_type 5 39.74 5282.9 1749.3
## - wkly_study_hours:math_score 2 88.07 5410.8 1749.5
## - practice_sport:math_score 2 98.15 5420.8 1750.5
## - wkly_study_hours:writing_score 2 99.05 5421.7 1750.7
## + ethnic_group:math_score 4 8.09 5314.6 1750.9
## + gender:ethnic_group 4 5.95 5316.7 1751.1
## + parent_educ:wkly_study_hours 10 104.49 5218.2 1752.1
## - parent_educ:practice_sport 10 268.47 5591.2 1752.8
## - ethnic_group:writing_score 4 173.82 5496.5 1754.7
## - parent_marital_status:wkly_study_hours 4 184.74 5507.4 1755.9
## - ethnic_group:lunch_type 4 241.75 5564.4 1762.0
## - ethnic_group:parent_marital_status 8 336.31 5659.0 1763.9
## - ethnic_group:parent_educ 20 580.45 5903.1 1764.8
##
## Step: AIC=1739.74
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## parent_marital_status:math_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:math_score 2 6.75 5365.4 1736.5
## - parent_marital_status:transport_means 2 6.92 5365.6 1736.5
## - ethnic_group:is_first_child 4 49.47 5408.1 1737.2
## - parent_educ:writing_score 5 67.87 5426.5 1737.2
## - gender:is_first_child 1 0.07 5358.7 1737.8
## - test_prep:writing_score 1 0.10 5358.7 1737.8
## - test_prep:math_score 1 0.14 5358.8 1737.8
## - transport_means:math_score 1 0.30 5358.9 1737.8
## - practice_sport:transport_means 2 18.99 5377.6 1737.8
## - is_first_child:wkly_study_hours 2 19.12 5377.8 1737.8
## - lunch_type:is_first_child 1 1.09 5359.7 1737.9
## - lunch_type:transport_means 1 1.34 5360.0 1737.9
## - ethnic_group:test_prep 4 56.21 5414.9 1737.9
## - is_first_child:writing_score 1 1.63 5360.3 1737.9
## - gender:test_prep 1 1.85 5360.5 1738.0
## - parent_marital_status:writing_score 2 20.34 5379.0 1738.0
## - gender:transport_means 1 2.26 5360.9 1738.0
## - lunch_type:practice_sport 2 23.96 5382.6 1738.4
## - is_first_child:math_score 1 6.35 5365.0 1738.4
## - parent_educ:is_first_child 5 80.26 5438.9 1738.5
## - parent_educ:transport_means 5 81.56 5440.2 1738.7
## - is_first_child:transport_means 1 10.60 5369.2 1738.9
## - transport_means:wkly_study_hours 2 31.07 5389.7 1739.2
## - parent_educ:parent_marital_status 12 217.16 5575.8 1739.2
## - gender:parent_marital_status 2 33.34 5392.0 1739.4
## - ethnic_group:practice_sport 8 144.67 5503.3 1739.5
## - transport_means:writing_score 1 16.33 5375.0 1739.5
## - gender:parent_educ 5 89.77 5448.4 1739.5
## - lunch_type:test_prep 1 17.71 5376.3 1739.7
## <none> 5358.6 1739.7
## - test_prep:parent_marital_status 2 36.93 5395.6 1739.8
## - writing_score:math_score 1 19.75 5378.4 1739.9
## - parent_marital_status:is_first_child 2 38.61 5397.2 1740.0
## - test_prep:is_first_child 1 21.29 5379.9 1740.1
## - test_prep:transport_means 1 24.99 5383.6 1740.5
## - lunch_type:parent_marital_status 2 43.46 5402.1 1740.5
## - lunch_type:math_score 1 29.57 5388.2 1741.0
## - parent_educ:math_score 5 105.92 5464.6 1741.3
## - gender:lunch_type 1 32.59 5391.2 1741.3
## - test_prep:practice_sport 2 51.04 5409.7 1741.3
## - practice_sport:is_first_child 2 51.99 5410.6 1741.4
## - lunch_type:wkly_study_hours 2 52.73 5411.4 1741.5
## - test_prep:wkly_study_hours 2 53.60 5412.2 1741.6
## - ethnic_group:transport_means 4 93.78 5452.4 1742.0
## - ethnic_group:wkly_study_hours 8 171.19 5529.8 1742.3
## - gender:math_score 1 42.05 5400.7 1742.3
## - gender:practice_sport 2 61.33 5420.0 1742.5
## - gender:writing_score 1 48.64 5407.3 1743.1
## - practice_sport:writing_score 2 67.16 5425.8 1743.1
## + practice_sport:wkly_study_hours 4 35.95 5322.7 1743.8
## - lunch_type:writing_score 1 57.04 5415.7 1744.0
## + parent_marital_status:practice_sport 4 29.09 5329.5 1744.5
## - parent_educ:test_prep 5 144.63 5503.3 1745.5
## - gender:wkly_study_hours 2 89.60 5448.2 1745.5
## + parent_educ:lunch_type 5 34.29 5324.3 1746.0
## - practice_sport:math_score 2 95.36 5454.0 1746.2
## - wkly_study_hours:math_score 2 95.95 5454.6 1746.2
## + ethnic_group:math_score 4 8.87 5349.8 1746.8
## + gender:ethnic_group 4 5.31 5353.3 1747.2
## + parent_educ:wkly_study_hours 10 111.66 5247.0 1747.3
## - wkly_study_hours:writing_score 2 109.57 5468.2 1747.7
## - parent_educ:practice_sport 10 260.25 5618.9 1747.7
## - parent_marital_status:wkly_study_hours 4 187.40 5546.0 1752.0
## - ethnic_group:writing_score 4 200.58 5559.2 1753.4
## - ethnic_group:lunch_type 4 241.00 5599.6 1757.7
## - ethnic_group:parent_educ 20 562.34 5921.0 1758.6
## - ethnic_group:parent_marital_status 8 333.71 5692.3 1759.4
##
## Step: AIC=1736.48
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:transport_means +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:transport_means +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:wkly_study_hours +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_marital_status:transport_means 2 7.82 5373.2 1733.3
## - ethnic_group:is_first_child 4 46.78 5412.2 1733.6
## - parent_educ:writing_score 5 65.75 5431.1 1733.7
## - parent_educ:parent_marital_status 13 218.65 5584.0 1734.0
## - test_prep:math_score 1 0.05 5365.4 1734.5
## - gender:is_first_child 1 0.17 5365.6 1734.5
## - transport_means:math_score 1 0.20 5365.6 1734.5
## - test_prep:writing_score 1 0.22 5365.6 1734.5
## - ethnic_group:test_prep 4 55.82 5421.2 1734.6
## - is_first_child:writing_score 1 1.38 5366.8 1734.6
## - lunch_type:transport_means 1 1.43 5366.8 1734.6
## - gender:test_prep 1 1.66 5367.0 1734.7
## - lunch_type:is_first_child 1 1.70 5367.1 1734.7
## - is_first_child:wkly_study_hours 2 19.95 5385.3 1734.7
## - practice_sport:transport_means 2 19.99 5385.4 1734.7
## - gender:transport_means 1 2.10 5367.5 1734.7
## - parent_educ:is_first_child 5 78.51 5443.9 1735.0
## - lunch_type:practice_sport 2 23.57 5389.0 1735.1
## - is_first_child:math_score 1 6.09 5371.5 1735.2
## - parent_educ:transport_means 5 81.96 5447.3 1735.4
## - parent_marital_status:writing_score 2 27.29 5392.7 1735.5
## - is_first_child:transport_means 1 11.04 5376.4 1735.7
## - ethnic_group:practice_sport 8 141.76 5507.1 1735.9
## - transport_means:wkly_study_hours 2 32.99 5398.4 1736.1
## - test_prep:parent_marital_status 2 33.08 5398.5 1736.1
## - transport_means:writing_score 1 15.38 5380.8 1736.2
## - lunch_type:test_prep 1 16.06 5381.4 1736.2
## <none> 5365.4 1736.5
## - parent_marital_status:is_first_child 2 37.06 5402.4 1736.5
## - writing_score:math_score 1 19.43 5384.8 1736.6
## - gender:parent_educ 5 93.47 5458.9 1736.7
## - gender:parent_marital_status 2 39.19 5404.6 1736.8
## - test_prep:is_first_child 1 22.38 5387.8 1736.9
## - test_prep:transport_means 1 25.63 5391.0 1737.3
## - lunch_type:math_score 1 27.25 5392.6 1737.5
## - parent_educ:math_score 5 102.69 5468.1 1737.7
## - gender:lunch_type 1 30.19 5395.6 1737.8
## - test_prep:practice_sport 2 50.07 5415.5 1738.0
## - practice_sport:is_first_child 2 51.54 5416.9 1738.1
## - lunch_type:wkly_study_hours 2 53.76 5419.1 1738.4
## - lunch_type:parent_marital_status 2 54.19 5419.6 1738.4
## - test_prep:wkly_study_hours 2 54.98 5420.4 1738.5
## - ethnic_group:transport_means 4 96.35 5461.7 1739.0
## - ethnic_group:wkly_study_hours 8 172.80 5538.2 1739.2
## - gender:math_score 1 44.06 5409.4 1739.3
## - gender:practice_sport 2 63.97 5429.4 1739.5
## + parent_marital_status:math_score 2 6.75 5358.6 1739.7
## - gender:writing_score 1 50.39 5415.8 1740.0
## - practice_sport:writing_score 2 69.85 5435.2 1740.1
## - lunch_type:writing_score 1 53.02 5418.4 1740.3
## + practice_sport:wkly_study_hours 4 34.38 5331.0 1740.7
## + parent_marital_status:practice_sport 4 27.79 5337.6 1741.4
## - parent_educ:test_prep 5 145.01 5510.4 1742.2
## - gender:wkly_study_hours 2 93.92 5459.3 1742.7
## + parent_educ:lunch_type 5 31.22 5334.2 1743.0
## - wkly_study_hours:math_score 2 99.25 5464.6 1743.3
## + ethnic_group:math_score 4 10.74 5354.6 1743.3
## - practice_sport:math_score 2 101.15 5466.5 1743.5
## + gender:ethnic_group 4 5.35 5360.0 1743.9
## + parent_educ:wkly_study_hours 10 110.59 5254.8 1744.2
## - wkly_study_hours:writing_score 2 112.00 5477.4 1744.7
## - parent_educ:practice_sport 10 267.55 5632.9 1745.2
## - parent_marital_status:wkly_study_hours 4 187.07 5552.4 1748.7
## - ethnic_group:writing_score 4 203.33 5568.7 1750.4
## - ethnic_group:lunch_type 4 241.21 5606.6 1754.4
## - ethnic_group:parent_educ 20 560.46 5925.8 1755.1
## - ethnic_group:parent_marital_status 9 352.61 5718.0 1756.0
##
## Step: AIC=1733.34
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:writing_score +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:writing_score 5 62.21 5435.4 1730.1
## - ethnic_group:is_first_child 4 49.66 5422.9 1730.8
## - is_first_child:wkly_study_hours 2 17.50 5390.7 1731.3
## - test_prep:math_score 1 0.04 5373.2 1731.3
## - test_prep:writing_score 1 0.24 5373.4 1731.4
## - transport_means:math_score 1 0.30 5373.5 1731.4
## - gender:is_first_child 1 0.40 5373.6 1731.4
## - is_first_child:writing_score 1 0.75 5374.0 1731.4
## - lunch_type:transport_means 1 1.60 5374.8 1731.5
## - gender:test_prep 1 1.65 5374.9 1731.5
## - lunch_type:is_first_child 1 1.89 5375.1 1731.5
## - gender:transport_means 1 1.95 5375.2 1731.6
## - ethnic_group:test_prep 4 57.94 5431.1 1731.7
## - is_first_child:math_score 1 4.83 5378.0 1731.9
## - practice_sport:transport_means 2 23.36 5396.6 1731.9
## - lunch_type:practice_sport 2 23.58 5396.8 1731.9
## - parent_educ:is_first_child 5 79.63 5452.8 1732.0
## - ethnic_group:practice_sport 8 138.61 5511.8 1732.4
## - gender:parent_marital_status 3 47.12 5420.3 1732.5
## - is_first_child:transport_means 1 10.85 5384.1 1732.5
## - parent_educ:transport_means 5 87.76 5461.0 1732.9
## - lunch_type:test_prep 1 15.02 5388.2 1733.0
## - transport_means:writing_score 1 15.13 5388.3 1733.0
## - transport_means:wkly_study_hours 2 33.71 5406.9 1733.0
## - test_prep:parent_marital_status 2 34.63 5407.8 1733.1
## - gender:parent_educ 5 90.19 5463.4 1733.2
## - parent_educ:parent_marital_status 14 259.65 5632.9 1733.2
## <none> 5373.2 1733.3
## - parent_marital_status:is_first_child 2 36.89 5410.1 1733.4
## - writing_score:math_score 1 21.54 5394.7 1733.7
## - test_prep:transport_means 1 22.24 5395.5 1733.8
## - test_prep:is_first_child 1 22.84 5396.0 1733.8
## - parent_educ:math_score 5 97.72 5470.9 1734.0
## - lunch_type:math_score 1 24.71 5397.9 1734.0
## - gender:lunch_type 1 28.29 5401.5 1734.4
## - practice_sport:is_first_child 2 48.85 5422.1 1734.7
## - test_prep:practice_sport 2 51.77 5425.0 1735.0
## - ethnic_group:transport_means 4 90.53 5463.7 1735.2
## - lunch_type:wkly_study_hours 2 55.67 5428.9 1735.4
## - test_prep:wkly_study_hours 2 58.01 5431.2 1735.7
## - gender:practice_sport 2 60.67 5433.9 1736.0
## - gender:math_score 1 43.56 5416.8 1736.1
## - ethnic_group:wkly_study_hours 8 175.34 5548.5 1736.3
## + parent_marital_status:transport_means 2 7.82 5365.4 1736.5
## + parent_marital_status:math_score 2 7.65 5365.6 1736.5
## - parent_marital_status:writing_score 3 85.53 5458.7 1736.7
## - practice_sport:writing_score 2 68.12 5441.3 1736.8
## - lunch_type:writing_score 1 50.08 5423.3 1736.8
## - gender:writing_score 1 51.32 5424.5 1737.0
## - lunch_type:parent_marital_status 3 96.14 5469.3 1737.8
## + practice_sport:wkly_study_hours 4 31.75 5341.5 1737.8
## + parent_marital_status:practice_sport 4 28.76 5344.4 1738.2
## - parent_educ:test_prep 5 142.60 5515.8 1738.8
## - gender:wkly_study_hours 2 96.52 5469.7 1739.8
## - practice_sport:math_score 2 97.50 5470.7 1740.0
## + ethnic_group:math_score 4 10.01 5363.2 1740.2
## + parent_educ:lunch_type 5 26.59 5346.6 1740.4
## + gender:ethnic_group 4 6.35 5366.9 1740.7
## - wkly_study_hours:math_score 2 105.20 5478.4 1740.8
## + parent_educ:wkly_study_hours 10 108.59 5264.6 1741.3
## - parent_educ:practice_sport 10 265.61 5638.8 1741.8
## - wkly_study_hours:writing_score 2 119.85 5493.1 1742.4
## - parent_marital_status:wkly_study_hours 5 184.32 5557.5 1743.2
## - ethnic_group:writing_score 4 220.03 5593.2 1749.0
## - ethnic_group:lunch_type 4 242.89 5616.1 1751.4
## - ethnic_group:parent_marital_status 10 362.53 5735.7 1751.9
## - ethnic_group:parent_educ 20 560.54 5933.7 1751.9
##
## Step: AIC=1730.14
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:is_first_child +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:is_first_child 4 49.50 5484.9 1727.5
## - is_first_child:wkly_study_hours 2 14.94 5450.4 1727.8
## - ethnic_group:test_prep 4 52.13 5487.5 1727.8
## - parent_educ:transport_means 5 74.03 5509.4 1728.1
## - test_prep:math_score 1 0.11 5435.5 1728.2
## - is_first_child:writing_score 1 0.40 5435.8 1728.2
## - transport_means:math_score 1 0.47 5435.9 1728.2
## - gender:test_prep 1 0.55 5436.0 1728.2
## - lunch_type:transport_means 1 0.60 5436.0 1728.2
## - lunch_type:is_first_child 1 0.62 5436.0 1728.2
## - gender:is_first_child 1 0.65 5436.1 1728.2
## - test_prep:writing_score 1 1.37 5436.8 1728.3
## - gender:transport_means 1 2.45 5437.9 1728.4
## - practice_sport:transport_means 2 22.14 5457.6 1728.5
## - is_first_child:math_score 1 4.16 5439.6 1728.6
## - transport_means:wkly_study_hours 2 25.62 5461.0 1728.9
## - lunch_type:practice_sport 2 25.99 5461.4 1729.0
## - parent_educ:parent_marital_status 14 256.02 5691.4 1729.3
## - gender:parent_marital_status 3 49.04 5484.4 1729.4
## - is_first_child:transport_means 1 12.12 5447.5 1729.5
## - lunch_type:test_prep 1 13.70 5449.1 1729.6
## - ethnic_group:practice_sport 8 145.66 5581.1 1729.7
## - transport_means:writing_score 1 16.37 5451.8 1729.9
## - gender:parent_educ 5 91.96 5527.4 1730.0
## <none> 5435.4 1730.1
## - test_prep:parent_marital_status 2 37.42 5472.8 1730.2
## - parent_educ:is_first_child 5 93.82 5529.2 1730.2
## - writing_score:math_score 1 19.83 5455.2 1730.3
## - test_prep:transport_means 1 21.10 5456.5 1730.4
## - lunch_type:math_score 1 21.62 5457.0 1730.5
## - gender:lunch_type 1 24.34 5459.8 1730.8
## - test_prep:practice_sport 2 45.03 5480.4 1731.0
## - test_prep:is_first_child 1 28.04 5463.5 1731.2
## - parent_marital_status:is_first_child 2 47.13 5482.5 1731.2
## - ethnic_group:wkly_study_hours 8 165.80 5601.2 1731.9
## - test_prep:wkly_study_hours 2 54.71 5490.1 1732.0
## - parent_educ:math_score 5 110.99 5546.4 1732.1
## - lunch_type:wkly_study_hours 2 55.35 5490.8 1732.1
## - ethnic_group:transport_means 4 96.71 5532.1 1732.5
## - lunch_type:writing_score 1 40.87 5476.3 1732.6
## - practice_sport:is_first_child 2 61.19 5496.6 1732.7
## - gender:practice_sport 2 63.54 5499.0 1733.0
## - practice_sport:writing_score 2 64.88 5500.3 1733.1
## + parent_educ:writing_score 5 62.21 5373.2 1733.3
## + parent_marital_status:math_score 2 5.37 5430.0 1733.5
## + parent_marital_status:transport_means 2 4.28 5431.1 1733.7
## - gender:math_score 1 54.88 5490.3 1734.1
## - parent_marital_status:writing_score 3 93.13 5528.5 1734.2
## + practice_sport:wkly_study_hours 4 35.09 5400.3 1734.3
## - gender:writing_score 1 62.81 5498.2 1734.9
## - lunch_type:parent_marital_status 3 102.72 5538.1 1735.2
## - gender:wkly_study_hours 2 84.05 5519.5 1735.2
## + parent_marital_status:practice_sport 4 26.59 5408.8 1735.2
## - wkly_study_hours:math_score 2 92.27 5527.7 1736.1
## - practice_sport:math_score 2 95.97 5531.4 1736.5
## + ethnic_group:math_score 4 9.81 5425.6 1737.1
## - parent_educ:test_prep 5 160.90 5596.3 1737.3
## - wkly_study_hours:writing_score 2 105.68 5541.1 1737.5
## + gender:ethnic_group 4 5.12 5430.3 1737.6
## - parent_educ:practice_sport 10 260.47 5695.9 1737.8
## + parent_educ:lunch_type 5 20.57 5414.8 1737.9
## + parent_educ:wkly_study_hours 10 107.36 5328.1 1738.4
## - parent_marital_status:wkly_study_hours 5 194.94 5630.4 1740.9
## - ethnic_group:writing_score 4 224.64 5660.1 1746.0
## - ethnic_group:lunch_type 4 234.65 5670.1 1747.1
## - ethnic_group:parent_educ 20 552.81 5988.2 1747.3
## - ethnic_group:parent_marital_status 10 363.05 5798.5 1748.3
##
## Step: AIC=1727.48
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:wkly_study_hours + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:wkly_study_hours 2 8.98 5493.9 1724.5
## - parent_educ:transport_means 5 67.47 5552.4 1724.7
## - ethnic_group:test_prep 4 49.82 5534.7 1724.8
## - test_prep:math_score 1 0.00 5484.9 1725.5
## - lunch_type:transport_means 1 0.01 5484.9 1725.5
## - is_first_child:writing_score 1 0.01 5484.9 1725.5
## - transport_means:math_score 1 0.03 5484.9 1725.5
## - gender:test_prep 1 0.54 5485.5 1725.5
## - lunch_type:is_first_child 1 0.72 5485.6 1725.6
## - is_first_child:math_score 1 0.76 5485.7 1725.6
## - test_prep:writing_score 1 0.84 5485.8 1725.6
## - gender:transport_means 1 1.08 5486.0 1725.6
## - practice_sport:transport_means 2 19.77 5504.7 1725.6
## - gender:is_first_child 1 2.62 5487.5 1725.8
## - transport_means:wkly_study_hours 2 23.06 5508.0 1726.0
## - parent_educ:parent_marital_status 14 254.99 5739.9 1726.3
## - gender:parent_marital_status 3 45.65 5530.6 1726.4
## - parent_educ:is_first_child 5 84.71 5569.6 1726.5
## - lunch_type:practice_sport 2 29.23 5514.1 1726.6
## - ethnic_group:practice_sport 8 143.06 5628.0 1726.7
## - transport_means:writing_score 1 13.35 5498.3 1726.9
## - lunch_type:test_prep 1 17.40 5502.3 1727.3
## <none> 5484.9 1727.5
## - lunch_type:math_score 1 19.17 5504.1 1727.5
## - test_prep:transport_means 1 21.54 5506.5 1727.8
## - gender:parent_educ 5 97.30 5582.2 1727.9
## - gender:lunch_type 1 22.29 5507.2 1727.9
## - writing_score:math_score 1 22.36 5507.3 1727.9
## - is_first_child:transport_means 1 22.89 5507.8 1727.9
## - parent_marital_status:is_first_child 2 41.76 5526.7 1728.0
## - test_prep:parent_marital_status 2 45.56 5530.5 1728.4
## - test_prep:practice_sport 2 45.66 5530.6 1728.4
## - test_prep:wkly_study_hours 2 46.50 5531.4 1728.5
## - ethnic_group:wkly_study_hours 8 161.99 5646.9 1728.7
## - test_prep:is_first_child 1 35.28 5520.2 1729.3
## - lunch_type:wkly_study_hours 2 54.73 5539.6 1729.3
## - lunch_type:writing_score 1 37.42 5522.3 1729.5
## - practice_sport:writing_score 2 61.59 5546.5 1730.1
## + ethnic_group:is_first_child 4 49.50 5435.4 1730.1
## - gender:practice_sport 2 62.26 5547.2 1730.1
## - practice_sport:is_first_child 2 64.05 5549.0 1730.3
## - gender:math_score 1 49.04 5534.0 1730.7
## + parent_educ:writing_score 5 62.05 5422.9 1730.8
## + parent_marital_status:transport_means 2 6.29 5478.6 1730.8
## - ethnic_group:transport_means 4 108.02 5592.9 1731.0
## + practice_sport:wkly_study_hours 4 40.60 5444.3 1731.1
## + parent_marital_status:math_score 2 3.37 5481.5 1731.1
## - parent_educ:math_score 5 128.64 5613.6 1731.2
## - parent_marital_status:writing_score 3 91.67 5576.6 1731.3
## - gender:writing_score 1 56.93 5541.8 1731.6
## - gender:wkly_study_hours 2 78.89 5563.8 1731.9
## - lunch_type:parent_marital_status 3 97.87 5582.8 1731.9
## - wkly_study_hours:math_score 2 83.40 5568.3 1732.4
## + parent_marital_status:practice_sport 4 28.17 5456.7 1732.5
## - practice_sport:math_score 2 95.91 5580.8 1733.7
## - parent_educ:test_prep 5 153.21 5638.1 1733.7
## - wkly_study_hours:writing_score 2 99.08 5584.0 1734.0
## + ethnic_group:math_score 4 6.41 5478.5 1734.8
## + gender:ethnic_group 4 3.54 5481.4 1735.1
## + parent_educ:lunch_type 5 19.41 5465.5 1735.4
## - parent_educ:practice_sport 10 267.31 5752.2 1735.6
## + parent_educ:wkly_study_hours 10 96.02 5388.9 1737.1
## - parent_marital_status:wkly_study_hours 5 199.26 5684.2 1738.5
## - ethnic_group:parent_educ 20 541.67 6026.6 1743.0
## - ethnic_group:writing_score 4 230.81 5715.7 1743.8
## - ethnic_group:lunch_type 4 254.22 5739.1 1746.2
## - ethnic_group:parent_marital_status 10 409.97 5894.9 1750.0
##
## Step: AIC=1724.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:test_prep + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - ethnic_group:test_prep 4 50.95 5544.8 1721.9
## - parent_educ:transport_means 5 72.69 5566.6 1722.2
## - transport_means:math_score 1 0.00 5493.9 1722.5
## - test_prep:math_score 1 0.02 5493.9 1722.5
## - lunch_type:transport_means 1 0.05 5493.9 1722.5
## - is_first_child:writing_score 1 0.06 5494.0 1722.5
## - is_first_child:math_score 1 0.30 5494.2 1722.5
## - practice_sport:transport_means 2 19.09 5513.0 1722.5
## - lunch_type:is_first_child 1 0.51 5494.4 1722.5
## - test_prep:writing_score 1 0.62 5494.5 1722.5
## - gender:test_prep 1 0.87 5494.8 1722.5
## - gender:transport_means 1 0.89 5494.8 1722.5
## - gender:is_first_child 1 3.17 5497.1 1722.8
## - parent_educ:parent_marital_status 14 252.13 5746.0 1722.9
## - transport_means:wkly_study_hours 2 24.78 5518.7 1723.1
## - gender:parent_marital_status 3 45.63 5539.5 1723.3
## - parent_educ:is_first_child 5 83.65 5577.5 1723.4
## - ethnic_group:practice_sport 8 142.97 5636.9 1723.6
## - transport_means:writing_score 1 12.78 5506.7 1723.8
## - lunch_type:practice_sport 2 32.32 5526.2 1723.9
## - lunch_type:test_prep 1 16.40 5510.3 1724.2
## <none> 5493.9 1724.5
## - gender:parent_educ 5 93.95 5587.8 1724.5
## - lunch_type:math_score 1 18.94 5512.8 1724.5
## - test_prep:transport_means 1 20.03 5513.9 1724.6
## - writing_score:math_score 1 21.34 5515.2 1724.7
## - gender:lunch_type 1 21.47 5515.4 1724.8
## - is_first_child:transport_means 1 23.56 5517.5 1725.0
## - test_prep:wkly_study_hours 2 42.48 5536.4 1725.0
## - parent_marital_status:is_first_child 2 42.64 5536.5 1725.0
## - test_prep:practice_sport 2 45.04 5538.9 1725.3
## - ethnic_group:wkly_study_hours 8 159.38 5653.3 1725.3
## - test_prep:parent_marital_status 2 46.18 5540.1 1725.4
## - lunch_type:writing_score 1 36.88 5530.8 1726.4
## - practice_sport:writing_score 2 56.79 5550.7 1726.5
## - lunch_type:wkly_study_hours 2 57.21 5551.1 1726.6
## - test_prep:is_first_child 1 39.32 5533.2 1726.7
## - gender:practice_sport 2 58.90 5552.8 1726.7
## - practice_sport:is_first_child 2 65.62 5559.5 1727.5
## + is_first_child:wkly_study_hours 2 8.98 5484.9 1727.5
## - gender:math_score 1 48.73 5542.6 1727.7
## + ethnic_group:is_first_child 4 43.55 5450.4 1727.8
## - ethnic_group:transport_means 4 107.39 5601.3 1727.9
## + parent_marital_status:transport_means 2 4.43 5489.5 1728.0
## + practice_sport:wkly_study_hours 4 41.43 5452.5 1728.0
## + parent_educ:writing_score 5 59.63 5434.3 1728.0
## + parent_marital_status:math_score 2 3.49 5490.4 1728.1
## - parent_marital_status:writing_score 3 91.40 5585.3 1728.2
## - gender:writing_score 1 56.13 5550.0 1728.5
## - gender:wkly_study_hours 2 75.86 5569.8 1728.5
## - lunch_type:parent_marital_status 3 96.95 5590.9 1728.8
## - parent_educ:math_score 5 135.88 5629.8 1728.9
## - wkly_study_hours:math_score 2 81.42 5575.3 1729.1
## + parent_marital_status:practice_sport 4 30.77 5463.1 1729.1
## - practice_sport:math_score 2 91.09 5585.0 1730.2
## - parent_educ:test_prep 5 151.58 5645.5 1730.5
## - wkly_study_hours:writing_score 2 97.71 5591.6 1730.8
## + ethnic_group:math_score 4 5.97 5487.9 1731.8
## + gender:ethnic_group 4 4.13 5489.8 1732.0
## + parent_educ:lunch_type 5 20.98 5472.9 1732.2
## - parent_educ:practice_sport 10 268.69 5762.6 1732.6
## + parent_educ:wkly_study_hours 10 96.11 5397.8 1734.0
## - parent_marital_status:wkly_study_hours 5 203.04 5696.9 1735.9
## - ethnic_group:parent_educ 20 540.16 6034.1 1739.8
## - ethnic_group:writing_score 4 235.62 5729.5 1741.2
## - ethnic_group:lunch_type 4 252.93 5746.8 1743.0
## - ethnic_group:parent_marital_status 10 413.83 5907.7 1747.3
##
## Step: AIC=1721.9
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:transport_means + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:transport_means 5 73.94 5618.8 1719.7
## - practice_sport:transport_means 2 18.67 5563.5 1719.9
## - lunch_type:transport_means 1 0.00 5544.8 1719.9
## - gender:transport_means 1 0.02 5544.9 1719.9
## - test_prep:writing_score 1 0.09 5544.9 1719.9
## - is_first_child:math_score 1 0.11 5545.0 1719.9
## - transport_means:wkly_study_hours 2 19.11 5564.0 1719.9
## - is_first_child:writing_score 1 0.29 5545.1 1719.9
## - transport_means:math_score 1 0.48 5545.3 1720.0
## - lunch_type:is_first_child 1 1.05 5545.9 1720.0
## - test_prep:math_score 1 1.13 5546.0 1720.0
## - gender:test_prep 1 1.61 5546.5 1720.1
## - gender:is_first_child 1 3.96 5548.8 1720.3
## - ethnic_group:practice_sport 8 137.21 5682.0 1720.3
## - transport_means:writing_score 1 8.26 5553.1 1720.8
## - gender:parent_marital_status 3 47.35 5592.2 1720.9
## - parent_educ:is_first_child 5 86.75 5631.6 1721.1
## - lunch_type:math_score 1 14.22 5559.1 1721.4
## - gender:parent_educ 5 90.41 5635.3 1721.4
## - parent_educ:parent_marital_status 14 265.70 5810.5 1721.5
## - lunch_type:practice_sport 2 34.53 5579.4 1721.6
## - gender:lunch_type 1 16.29 5561.1 1721.6
## - lunch_type:test_prep 1 18.11 5563.0 1721.8
## <none> 5544.8 1721.9
## - test_prep:wkly_study_hours 2 38.73 5583.6 1722.0
## - test_prep:transport_means 1 22.21 5567.1 1722.2
## - writing_score:math_score 1 23.54 5568.4 1722.4
## - test_prep:practice_sport 2 43.67 5588.5 1722.5
## - parent_marital_status:is_first_child 2 44.25 5589.1 1722.6
## - is_first_child:transport_means 1 25.71 5570.6 1722.6
## - test_prep:parent_marital_status 2 47.89 5592.7 1723.0
## - practice_sport:writing_score 2 49.93 5594.8 1723.2
## - gender:practice_sport 2 51.64 5596.5 1723.4
## - lunch_type:writing_score 1 33.99 5578.8 1723.5
## - practice_sport:is_first_child 2 53.57 5598.4 1723.6
## - lunch_type:wkly_study_hours 2 58.06 5602.9 1724.0
## - test_prep:is_first_child 1 40.92 5585.8 1724.2
## + ethnic_group:test_prep 4 50.95 5493.9 1724.5
## + is_first_child:wkly_study_hours 2 10.11 5534.7 1724.8
## - gender:math_score 1 47.04 5591.9 1724.9
## - parent_educ:math_score 5 125.85 5670.7 1725.1
## + parent_marital_status:transport_means 2 6.66 5538.2 1725.2
## - gender:wkly_study_hours 2 70.75 5615.6 1725.4
## + practice_sport:wkly_study_hours 4 41.94 5502.9 1725.4
## - ethnic_group:transport_means 4 109.52 5654.4 1725.4
## - gender:writing_score 1 53.05 5597.9 1725.5
## + parent_marital_status:math_score 2 3.50 5541.3 1725.5
## + ethnic_group:is_first_child 4 40.43 5504.4 1725.6
## - ethnic_group:wkly_study_hours 8 191.07 5735.9 1725.9
## - wkly_study_hours:math_score 2 77.76 5622.6 1726.1
## + parent_educ:writing_score 5 53.48 5491.4 1726.2
## - parent_marital_status:writing_score 3 97.54 5642.4 1726.2
## + parent_marital_status:practice_sport 4 34.33 5510.5 1726.2
## - practice_sport:math_score 2 79.54 5624.4 1726.3
## - lunch_type:parent_marital_status 3 100.88 5645.7 1726.5
## - parent_educ:test_prep 5 139.67 5684.5 1726.6
## - wkly_study_hours:writing_score 2 91.86 5636.7 1727.6
## - parent_educ:practice_sport 10 264.05 5808.9 1729.3
## + ethnic_group:math_score 4 3.80 5541.0 1729.5
## + parent_educ:lunch_type 5 22.03 5522.8 1729.5
## + gender:ethnic_group 4 2.81 5542.0 1729.6
## + parent_educ:wkly_study_hours 10 109.21 5435.6 1730.2
## - parent_marital_status:wkly_study_hours 5 207.68 5752.5 1733.6
## - ethnic_group:parent_educ 20 568.34 6113.2 1739.5
## - ethnic_group:writing_score 4 258.59 5803.4 1740.8
## - ethnic_group:lunch_type 4 261.59 5806.4 1741.1
## - ethnic_group:parent_marital_status 10 402.96 5947.8 1743.3
##
## Step: AIC=1719.71
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:transport_means + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:transport_means 2 12.44 5631.2 1717.0
## - gender:transport_means 1 0.08 5618.9 1717.7
## - is_first_child:writing_score 1 0.15 5618.9 1717.7
## - test_prep:writing_score 1 0.25 5619.0 1717.7
## - transport_means:math_score 1 0.30 5619.1 1717.7
## - lunch_type:transport_means 1 0.42 5619.2 1717.8
## - test_prep:math_score 1 0.65 5619.4 1717.8
## - lunch_type:is_first_child 1 0.83 5619.6 1717.8
## - transport_means:wkly_study_hours 2 19.99 5638.8 1717.8
## - gender:test_prep 1 0.98 5619.8 1717.8
## - is_first_child:math_score 1 1.48 5620.3 1717.9
## - gender:is_first_child 1 1.48 5620.3 1717.9
## - parent_educ:is_first_child 5 80.44 5699.2 1718.1
## - gender:parent_educ 5 82.21 5701.0 1718.3
## - gender:parent_marital_status 3 44.63 5663.4 1718.4
## - parent_educ:parent_marital_status 14 260.26 5879.0 1718.4
## - ethnic_group:practice_sport 8 143.17 5762.0 1718.6
## - transport_means:writing_score 1 8.99 5627.8 1718.7
## - gender:lunch_type 1 10.12 5628.9 1718.8
## - lunch_type:math_score 1 11.04 5629.8 1718.9
## - lunch_type:test_prep 1 14.11 5632.9 1719.2
## - test_prep:transport_means 1 17.85 5636.6 1719.6
## <none> 5618.8 1719.7
## - test_prep:wkly_study_hours 2 38.99 5657.8 1719.8
## - test_prep:practice_sport 2 39.70 5658.5 1719.9
## - writing_score:math_score 1 21.31 5640.1 1719.9
## - lunch_type:practice_sport 2 42.28 5661.1 1720.1
## - lunch_type:writing_score 1 26.65 5645.4 1720.5
## - is_first_child:transport_means 1 29.62 5648.4 1720.8
## - practice_sport:is_first_child 2 49.76 5668.5 1720.9
## - test_prep:parent_marital_status 2 50.29 5669.1 1721.0
## - lunch_type:wkly_study_hours 2 52.61 5671.4 1721.2
## - parent_marital_status:is_first_child 2 52.99 5671.8 1721.2
## - practice_sport:writing_score 2 58.82 5677.6 1721.9
## + parent_educ:transport_means 5 73.94 5544.8 1721.9
## + is_first_child:wkly_study_hours 2 16.30 5602.5 1722.0
## + ethnic_group:test_prep 4 52.20 5566.6 1722.2
## - parent_educ:math_score 5 120.87 5739.7 1722.3
## + parent_marital_status:transport_means 2 11.51 5607.3 1722.5
## - gender:math_score 1 45.81 5664.6 1722.5
## - gender:practice_sport 2 65.10 5683.9 1722.5
## - test_prep:is_first_child 1 46.36 5665.1 1722.6
## - ethnic_group:transport_means 4 106.47 5725.3 1722.8
## - parent_educ:test_prep 5 126.73 5745.5 1722.9
## - gender:writing_score 1 51.73 5670.5 1723.1
## - lunch_type:parent_marital_status 3 91.10 5709.9 1723.2
## + parent_marital_status:math_score 2 4.77 5614.0 1723.2
## - wkly_study_hours:math_score 2 75.00 5693.8 1723.5
## - gender:wkly_study_hours 2 75.34 5694.1 1723.6
## + practice_sport:wkly_study_hours 4 39.19 5579.6 1723.6
## - parent_marital_status:writing_score 3 96.44 5715.2 1723.8
## - parent_educ:practice_sport 10 237.94 5856.7 1724.2
## + parent_marital_status:practice_sport 4 33.25 5585.5 1724.2
## + ethnic_group:is_first_child 4 31.89 5586.9 1724.3
## - wkly_study_hours:writing_score 2 86.03 5704.8 1724.7
## - practice_sport:math_score 2 86.82 5705.6 1724.8
## - ethnic_group:wkly_study_hours 8 204.46 5823.2 1724.8
## + parent_educ:writing_score 5 40.28 5578.5 1725.5
## + gender:ethnic_group 4 5.99 5612.8 1727.1
## + ethnic_group:math_score 4 3.53 5615.3 1727.3
## + parent_educ:lunch_type 5 17.71 5601.1 1727.8
## + parent_educ:wkly_study_hours 10 104.72 5514.1 1728.6
## - parent_marital_status:wkly_study_hours 5 200.09 5818.9 1730.4
## - ethnic_group:parent_educ 20 545.75 6164.5 1734.4
## - ethnic_group:lunch_type 4 234.14 5852.9 1735.8
## - ethnic_group:writing_score 4 237.08 5855.9 1736.1
## - ethnic_group:parent_marital_status 10 432.17 6051.0 1743.4
##
## Step: AIC=1717.02
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:is_first_child +
## parent_educ:math_score + lunch_type:test_prep + lunch_type:parent_marital_status +
## lunch_type:practice_sport + lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - parent_educ:is_first_child 5 76.61 5707.8 1715.0
## - gender:transport_means 1 0.02 5631.2 1715.0
## - test_prep:writing_score 1 0.05 5631.3 1715.0
## - lunch_type:transport_means 1 0.39 5631.6 1715.1
## - transport_means:math_score 1 0.41 5631.6 1715.1
## - is_first_child:writing_score 1 0.55 5631.8 1715.1
## - gender:is_first_child 1 0.58 5631.8 1715.1
## - transport_means:wkly_study_hours 2 19.72 5650.9 1715.1
## - lunch_type:is_first_child 1 0.65 5631.9 1715.1
## - test_prep:math_score 1 1.28 5632.5 1715.2
## - gender:parent_educ 5 78.20 5709.4 1715.2
## - gender:test_prep 1 1.52 5632.7 1715.2
## - is_first_child:math_score 1 2.54 5633.8 1715.3
## - ethnic_group:practice_sport 8 139.44 5770.7 1715.5
## - gender:parent_marital_status 3 44.60 5675.8 1715.7
## - transport_means:writing_score 1 8.58 5639.8 1715.9
## - gender:lunch_type 1 10.13 5641.4 1716.1
## - lunch_type:math_score 1 10.99 5642.2 1716.2
## - test_prep:transport_means 1 15.79 5647.0 1716.7
## - parent_educ:parent_marital_status 14 271.11 5902.3 1716.8
## - lunch_type:test_prep 1 16.94 5648.2 1716.8
## - test_prep:wkly_study_hours 2 37.83 5669.0 1717.0
## <none> 5631.2 1717.0
## - test_prep:practice_sport 2 40.42 5671.6 1717.2
## - writing_score:math_score 1 21.75 5653.0 1717.3
## - lunch_type:practice_sport 2 42.95 5674.2 1717.5
## - practice_sport:is_first_child 2 45.77 5677.0 1717.8
## - lunch_type:writing_score 1 26.71 5657.9 1717.8
## - test_prep:parent_marital_status 2 51.42 5682.6 1718.4
## - practice_sport:writing_score 2 52.61 5683.8 1718.5
## - is_first_child:transport_means 1 35.50 5666.7 1718.7
## - lunch_type:wkly_study_hours 2 55.18 5686.4 1718.8
## - parent_marital_status:is_first_child 2 56.95 5688.2 1719.0
## - gender:practice_sport 2 59.72 5690.9 1719.2
## + is_first_child:wkly_study_hours 2 14.80 5616.4 1719.5
## + ethnic_group:test_prep 4 52.63 5578.6 1719.5
## - test_prep:is_first_child 1 43.24 5674.5 1719.5
## + parent_marital_status:transport_means 2 13.34 5617.9 1719.6
## + practice_sport:transport_means 2 12.44 5618.8 1719.7
## - gender:math_score 1 46.07 5677.3 1719.8
## - parent_educ:math_score 5 123.58 5754.8 1719.8
## + parent_educ:transport_means 5 67.71 5563.5 1719.9
## - ethnic_group:transport_means 4 106.18 5737.4 1720.0
## - parent_educ:test_prep 5 126.08 5757.3 1720.1
## - gender:writing_score 1 50.52 5681.7 1720.3
## - lunch_type:parent_marital_status 3 89.48 5720.7 1720.3
## + parent_marital_status:math_score 2 5.67 5625.6 1720.4
## - wkly_study_hours:math_score 2 72.34 5703.6 1720.5
## - gender:wkly_study_hours 2 73.01 5704.2 1720.6
## - parent_marital_status:writing_score 3 94.41 5725.6 1720.8
## + practice_sport:wkly_study_hours 4 39.22 5592.0 1720.9
## - practice_sport:math_score 2 78.17 5709.4 1721.2
## - wkly_study_hours:writing_score 2 82.68 5713.9 1721.6
## + parent_marital_status:practice_sport 4 32.00 5599.2 1721.7
## + ethnic_group:is_first_child 4 31.24 5600.0 1721.7
## - ethnic_group:wkly_study_hours 8 204.12 5835.3 1722.0
## + parent_educ:writing_score 5 39.07 5592.2 1722.9
## - parent_educ:practice_sport 10 263.04 5894.3 1724.0
## + gender:ethnic_group 4 6.02 5625.2 1724.4
## + ethnic_group:math_score 4 3.58 5627.6 1724.6
## + parent_educ:lunch_type 5 17.31 5613.9 1725.2
## + parent_educ:wkly_study_hours 10 106.46 5524.8 1725.8
## - parent_marital_status:wkly_study_hours 5 211.62 5842.8 1728.8
## - ethnic_group:writing_score 4 230.12 5861.3 1732.7
## - ethnic_group:lunch_type 4 232.75 5864.0 1732.9
## - ethnic_group:parent_educ 20 561.30 6192.5 1733.1
## - ethnic_group:parent_marital_status 10 438.60 6069.8 1741.3
##
## Step: AIC=1714.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:transport_means + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:transport_means 1 0.01 5707.8 1713.0
## - test_prep:writing_score 1 0.15 5708.0 1713.0
## - is_first_child:math_score 1 0.27 5708.1 1713.0
## - transport_means:math_score 1 0.53 5708.4 1713.0
## - is_first_child:writing_score 1 1.29 5709.1 1713.1
## - lunch_type:transport_means 1 1.38 5709.2 1713.1
## - gender:test_prep 1 1.70 5709.5 1713.2
## - test_prep:math_score 1 2.61 5710.4 1713.3
## - lunch_type:is_first_child 1 3.12 5711.0 1713.3
## - gender:is_first_child 1 4.45 5712.3 1713.5
## - transport_means:wkly_study_hours 2 26.24 5734.1 1713.7
## - transport_means:writing_score 1 7.06 5714.9 1713.7
## - ethnic_group:practice_sport 8 146.35 5854.2 1713.9
## - gender:parent_marital_status 3 48.88 5756.7 1714.0
## - lunch_type:math_score 1 10.29 5718.1 1714.0
## - gender:lunch_type 1 10.90 5718.7 1714.1
## - test_prep:transport_means 1 12.71 5720.5 1714.3
## - writing_score:math_score 1 16.70 5724.5 1714.7
## - lunch_type:test_prep 1 17.61 5725.4 1714.8
## - test_prep:wkly_study_hours 2 37.92 5745.8 1714.9
## <none> 5707.8 1715.0
## - lunch_type:practice_sport 2 39.42 5747.3 1715.0
## - test_prep:practice_sport 2 39.70 5747.5 1715.1
## - lunch_type:writing_score 1 24.64 5732.5 1715.5
## - practice_sport:is_first_child 2 44.32 5752.2 1715.5
## - practice_sport:writing_score 2 54.68 5762.5 1716.6
## - gender:parent_educ 5 114.58 5822.4 1716.7
## - gender:math_score 1 37.43 5745.3 1716.8
## - gender:writing_score 1 37.56 5745.4 1716.9
## - is_first_child:transport_means 1 38.28 5746.1 1716.9
## + parent_educ:is_first_child 5 76.61 5631.2 1717.0
## - test_prep:parent_marital_status 2 60.46 5768.3 1717.2
## - lunch_type:wkly_study_hours 2 60.62 5768.5 1717.2
## + ethnic_group:test_prep 4 55.40 5652.4 1717.2
## + parent_marital_status:transport_means 2 15.40 5692.4 1717.4
## - parent_educ:parent_marital_status 14 304.41 6012.2 1717.6
## + is_first_child:wkly_study_hours 2 12.69 5695.1 1717.7
## - ethnic_group:transport_means 4 105.20 5813.0 1717.8
## - gender:practice_sport 2 66.04 5773.9 1717.8
## + practice_sport:wkly_study_hours 4 49.34 5658.5 1717.9
## + practice_sport:transport_means 2 8.61 5699.2 1718.1
## - parent_marital_status:is_first_child 2 71.31 5779.1 1718.3
## - lunch_type:parent_marital_status 3 90.99 5798.8 1718.3
## - parent_educ:math_score 5 132.47 5840.3 1718.5
## + parent_educ:transport_means 5 61.88 5646.0 1718.6
## + parent_marital_status:math_score 2 3.43 5704.4 1718.6
## - test_prep:is_first_child 1 58.78 5766.6 1719.0
## - parent_educ:test_prep 5 138.60 5846.4 1719.1
## - wkly_study_hours:math_score 2 80.15 5788.0 1719.2
## - parent_marital_status:writing_score 3 102.30 5810.1 1719.5
## + parent_marital_status:practice_sport 4 31.21 5676.6 1719.8
## - gender:wkly_study_hours 2 86.41 5794.2 1719.8
## - practice_sport:math_score 2 86.57 5794.4 1719.9
## + parent_educ:writing_score 5 48.93 5658.9 1719.9
## + ethnic_group:is_first_child 4 25.75 5682.1 1720.3
## - wkly_study_hours:writing_score 2 92.28 5800.1 1720.5
## - ethnic_group:wkly_study_hours 8 215.01 5922.8 1720.8
## + ethnic_group:math_score 4 7.13 5700.7 1722.2
## + gender:ethnic_group 4 4.96 5702.9 1722.5
## - parent_educ:practice_sport 10 273.62 5981.5 1722.6
## + parent_educ:lunch_type 5 16.87 5691.0 1723.2
## + parent_educ:wkly_study_hours 10 110.41 5597.4 1723.5
## - parent_marital_status:wkly_study_hours 5 212.41 5920.2 1726.5
## - ethnic_group:writing_score 4 208.55 5916.4 1728.2
## - ethnic_group:parent_educ 20 559.42 6267.3 1730.2
## - ethnic_group:lunch_type 4 230.04 5937.9 1730.3
## - ethnic_group:parent_marital_status 10 449.91 6157.7 1739.8
##
## Step: AIC=1712.99
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:writing_score + test_prep:math_score +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## is_first_child:math_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - test_prep:writing_score 1 0.16 5708.0 1711.0
## - is_first_child:math_score 1 0.26 5708.1 1711.0
## - is_first_child:writing_score 1 1.31 5709.2 1711.1
## - lunch_type:transport_means 1 1.37 5709.2 1711.1
## - transport_means:math_score 1 1.53 5709.4 1711.2
## - gender:test_prep 1 1.75 5709.6 1711.2
## - test_prep:math_score 1 2.66 5710.5 1711.3
## - lunch_type:is_first_child 1 3.11 5711.0 1711.3
## - gender:is_first_child 1 4.45 5712.3 1711.5
## - transport_means:wkly_study_hours 2 26.26 5734.1 1711.7
## - ethnic_group:practice_sport 8 146.97 5854.8 1712.0
## - gender:parent_marital_status 3 48.88 5756.7 1712.0
## - lunch_type:math_score 1 10.28 5718.1 1712.0
## - gender:lunch_type 1 10.89 5718.7 1712.1
## - test_prep:transport_means 1 14.07 5721.9 1712.4
## - writing_score:math_score 1 16.70 5724.5 1712.7
## - transport_means:writing_score 1 17.57 5725.4 1712.8
## - lunch_type:test_prep 1 17.60 5725.4 1712.8
## - test_prep:wkly_study_hours 2 37.92 5745.8 1712.9
## <none> 5707.8 1713.0
## - lunch_type:practice_sport 2 39.47 5747.3 1713.1
## - test_prep:practice_sport 2 39.70 5747.5 1713.1
## - lunch_type:writing_score 1 24.66 5732.5 1713.5
## - practice_sport:is_first_child 2 44.37 5752.2 1713.6
## - practice_sport:writing_score 2 54.87 5762.7 1714.6
## - gender:parent_educ 5 114.61 5822.5 1714.7
## - gender:math_score 1 37.46 5745.3 1714.8
## - gender:writing_score 1 37.56 5745.4 1714.9
## - is_first_child:transport_means 1 38.36 5746.2 1714.9
## + gender:transport_means 1 0.01 5707.8 1715.0
## + parent_educ:is_first_child 5 76.60 5631.2 1715.0
## - test_prep:parent_marital_status 2 60.48 5768.3 1715.2
## - lunch_type:wkly_study_hours 2 60.72 5768.6 1715.2
## + ethnic_group:test_prep 4 54.54 5653.3 1715.3
## + parent_marital_status:transport_means 2 15.30 5692.5 1715.4
## - parent_educ:parent_marital_status 14 304.60 6012.4 1715.7
## + is_first_child:wkly_study_hours 2 12.67 5695.2 1715.7
## - gender:practice_sport 2 66.34 5774.2 1715.8
## + practice_sport:wkly_study_hours 4 49.27 5658.6 1715.9
## - ethnic_group:transport_means 4 106.54 5814.4 1715.9
## + practice_sport:transport_means 2 8.58 5699.3 1716.1
## - parent_marital_status:is_first_child 2 71.40 5779.2 1716.3
## - lunch_type:parent_marital_status 3 91.10 5798.9 1716.3
## + parent_educ:transport_means 5 61.87 5646.0 1716.6
## - parent_educ:math_score 5 133.46 5841.3 1716.6
## + parent_marital_status:math_score 2 3.41 5704.4 1716.6
## - test_prep:is_first_child 1 58.88 5766.7 1717.0
## - parent_educ:test_prep 5 138.91 5846.8 1717.2
## - wkly_study_hours:math_score 2 80.43 5788.3 1717.2
## - parent_marital_status:writing_score 3 102.30 5810.1 1717.5
## + parent_marital_status:practice_sport 4 31.21 5676.6 1717.8
## - gender:wkly_study_hours 2 86.68 5794.5 1717.9
## - practice_sport:math_score 2 86.74 5794.6 1717.9
## + parent_educ:writing_score 5 48.93 5658.9 1717.9
## + ethnic_group:is_first_child 4 25.65 5682.2 1718.3
## - wkly_study_hours:writing_score 2 92.59 5800.4 1718.5
## - ethnic_group:wkly_study_hours 8 215.02 5922.9 1718.8
## + ethnic_group:math_score 4 7.13 5700.7 1720.2
## + gender:ethnic_group 4 4.95 5702.9 1720.5
## - parent_educ:practice_sport 10 273.79 5981.6 1720.6
## + parent_educ:lunch_type 5 16.87 5691.0 1721.2
## + parent_educ:wkly_study_hours 10 110.39 5597.5 1721.5
## - parent_marital_status:wkly_study_hours 5 212.46 5920.3 1724.5
## - ethnic_group:writing_score 4 209.20 5917.0 1726.2
## - ethnic_group:parent_educ 20 559.42 6267.3 1728.2
## - ethnic_group:lunch_type 4 230.06 5937.9 1728.3
## - ethnic_group:parent_marital_status 10 451.07 6158.9 1737.9
##
## Step: AIC=1711.01
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + is_first_child:math_score +
## transport_means:wkly_study_hours + transport_means:writing_score +
## transport_means:math_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:math_score 1 0.24 5708.2 1709.0
## - lunch_type:transport_means 1 1.34 5709.3 1709.1
## - is_first_child:writing_score 1 1.37 5709.4 1709.2
## - transport_means:math_score 1 1.51 5709.5 1709.2
## - gender:test_prep 1 2.58 5710.6 1709.3
## - lunch_type:is_first_child 1 3.11 5711.1 1709.3
## - gender:is_first_child 1 4.48 5712.5 1709.5
## - transport_means:wkly_study_hours 2 26.18 5734.2 1709.7
## - test_prep:math_score 1 8.18 5716.2 1709.8
## - gender:parent_marital_status 3 48.73 5756.7 1710.0
## - ethnic_group:practice_sport 8 147.33 5855.3 1710.0
## - lunch_type:math_score 1 10.57 5718.6 1710.1
## - gender:lunch_type 1 11.37 5719.4 1710.2
## - test_prep:transport_means 1 13.97 5722.0 1710.5
## - writing_score:math_score 1 16.90 5724.9 1710.8
## - lunch_type:test_prep 1 17.52 5725.5 1710.8
## - transport_means:writing_score 1 17.77 5725.8 1710.8
## - test_prep:wkly_study_hours 2 37.81 5745.8 1710.9
## <none> 5708.0 1711.0
## - test_prep:practice_sport 2 39.84 5747.8 1711.1
## - lunch_type:practice_sport 2 39.86 5747.9 1711.1
## - practice_sport:is_first_child 2 44.42 5752.4 1711.6
## - lunch_type:writing_score 1 25.50 5733.5 1711.6
## - practice_sport:writing_score 2 54.91 5762.9 1712.7
## - gender:math_score 1 37.35 5745.4 1712.8
## - gender:writing_score 1 37.43 5745.4 1712.9
## - gender:parent_educ 5 116.10 5824.1 1712.9
## - is_first_child:transport_means 1 38.50 5746.5 1713.0
## + test_prep:writing_score 1 0.16 5707.8 1713.0
## + gender:transport_means 1 0.02 5708.0 1713.0
## + parent_educ:is_first_child 5 76.71 5631.3 1713.0
## - test_prep:parent_marital_status 2 60.42 5768.4 1713.2
## - lunch_type:wkly_study_hours 2 60.56 5768.6 1713.2
## + ethnic_group:test_prep 4 54.69 5653.3 1713.3
## + parent_marital_status:transport_means 2 15.18 5692.8 1713.4
## + is_first_child:wkly_study_hours 2 12.71 5695.3 1713.7
## - gender:practice_sport 2 66.77 5774.8 1713.9
## - parent_educ:parent_marital_status 14 306.63 6014.6 1713.9
## + practice_sport:wkly_study_hours 4 49.28 5658.7 1713.9
## - ethnic_group:transport_means 4 106.39 5814.4 1713.9
## + practice_sport:transport_means 2 8.70 5699.3 1714.1
## - parent_marital_status:is_first_child 2 71.25 5779.3 1714.3
## - lunch_type:parent_marital_status 3 90.95 5799.0 1714.3
## + parent_educ:transport_means 5 61.73 5646.3 1714.6
## + parent_marital_status:math_score 2 3.26 5704.7 1714.7
## - parent_educ:math_score 5 133.91 5841.9 1714.7
## - test_prep:is_first_child 1 58.77 5766.8 1715.0
## - parent_educ:test_prep 5 138.87 5846.9 1715.2
## - wkly_study_hours:math_score 2 80.27 5788.3 1715.2
## - parent_marital_status:writing_score 3 102.59 5810.6 1715.5
## + parent_marital_status:practice_sport 4 30.77 5677.2 1715.8
## - gender:wkly_study_hours 2 86.54 5794.5 1715.9
## - practice_sport:math_score 2 86.86 5794.9 1715.9
## + parent_educ:writing_score 5 47.96 5660.0 1716.0
## + ethnic_group:is_first_child 4 25.80 5682.2 1716.3
## - wkly_study_hours:writing_score 2 92.44 5800.4 1716.5
## - ethnic_group:wkly_study_hours 8 214.87 5922.9 1716.8
## + ethnic_group:math_score 4 7.12 5700.9 1718.3
## + gender:ethnic_group 4 4.92 5703.1 1718.5
## - parent_educ:practice_sport 10 274.10 5982.1 1718.7
## + parent_educ:lunch_type 5 17.03 5691.0 1719.2
## + parent_educ:wkly_study_hours 10 109.64 5598.4 1719.6
## - parent_marital_status:wkly_study_hours 5 212.84 5920.8 1722.6
## - ethnic_group:writing_score 4 209.86 5917.9 1724.3
## - ethnic_group:parent_educ 20 559.78 6267.8 1726.2
## - ethnic_group:lunch_type 4 229.91 5937.9 1726.3
## - ethnic_group:parent_marital_status 10 451.90 6159.9 1736.0
##
## Step: AIC=1709.03
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:transport_means +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:transport_means 1 1.27 5709.5 1707.2
## - transport_means:math_score 1 1.56 5709.8 1707.2
## - gender:test_prep 1 2.56 5710.8 1707.3
## - lunch_type:is_first_child 1 2.89 5711.1 1707.3
## - transport_means:wkly_study_hours 2 26.35 5734.6 1707.8
## - test_prep:math_score 1 8.05 5716.3 1707.9
## - gender:parent_marital_status 3 48.53 5756.8 1708.0
## - ethnic_group:practice_sport 8 147.30 5855.5 1708.1
## - lunch_type:math_score 1 10.42 5718.7 1708.1
## - gender:lunch_type 1 11.23 5719.5 1708.2
## - test_prep:transport_means 1 13.88 5722.1 1708.5
## - gender:is_first_child 1 13.91 5722.2 1708.5
## - is_first_child:writing_score 1 16.29 5724.5 1708.7
## - writing_score:math_score 1 16.93 5725.2 1708.8
## - transport_means:writing_score 1 17.54 5725.8 1708.8
## - lunch_type:test_prep 1 17.55 5725.8 1708.8
## - test_prep:wkly_study_hours 2 38.73 5747.0 1709.0
## <none> 5708.2 1709.0
## - lunch_type:practice_sport 2 39.87 5748.1 1709.1
## - test_prep:practice_sport 2 39.91 5748.1 1709.1
## - lunch_type:writing_score 1 25.27 5733.5 1709.6
## - practice_sport:is_first_child 2 45.31 5753.5 1709.7
## - practice_sport:writing_score 2 55.07 5763.3 1710.7
## - gender:math_score 1 37.12 5745.4 1710.9
## - gender:writing_score 1 37.27 5745.5 1710.9
## - gender:parent_educ 5 116.14 5824.4 1710.9
## - is_first_child:transport_means 1 38.45 5746.7 1711.0
## + is_first_child:math_score 1 0.24 5708.0 1711.0
## + test_prep:writing_score 1 0.13 5708.1 1711.0
## + gender:transport_means 1 0.01 5708.2 1711.0
## - test_prep:parent_marital_status 2 60.18 5768.4 1711.2
## - lunch_type:wkly_study_hours 2 60.64 5768.9 1711.3
## + parent_educ:is_first_child 5 74.37 5633.9 1711.3
## + ethnic_group:test_prep 4 54.48 5653.8 1711.4
## + parent_marital_status:transport_means 2 14.94 5693.3 1711.5
## + is_first_child:wkly_study_hours 2 12.16 5696.1 1711.8
## - parent_educ:parent_marital_status 14 306.48 6014.7 1711.9
## - gender:practice_sport 2 66.78 5775.0 1711.9
## + practice_sport:wkly_study_hours 4 47.93 5660.3 1712.1
## + practice_sport:transport_means 2 8.91 5699.3 1712.1
## - ethnic_group:transport_means 4 108.26 5816.5 1712.1
## - parent_marital_status:is_first_child 2 71.06 5779.3 1712.3
## - lunch_type:parent_marital_status 3 90.83 5799.1 1712.3
## + parent_educ:transport_means 5 61.90 5646.3 1712.6
## + parent_marital_status:math_score 2 3.24 5705.0 1712.7
## - parent_educ:math_score 5 134.51 5842.7 1712.8
## - parent_educ:test_prep 5 139.45 5847.7 1713.3
## - wkly_study_hours:math_score 2 82.11 5790.4 1713.5
## - parent_marital_status:writing_score 3 102.40 5810.6 1713.5
## - test_prep:is_first_child 1 65.12 5773.4 1713.7
## + parent_marital_status:practice_sport 4 30.99 5677.2 1713.8
## - gender:wkly_study_hours 2 86.99 5795.2 1714.0
## - practice_sport:math_score 2 87.20 5795.4 1714.0
## + parent_educ:writing_score 5 47.21 5661.0 1714.1
## + ethnic_group:is_first_child 4 24.50 5683.7 1714.5
## - wkly_study_hours:writing_score 2 94.32 5802.6 1714.7
## - ethnic_group:wkly_study_hours 8 214.85 5923.1 1714.8
## + ethnic_group:math_score 4 7.13 5701.1 1716.3
## + gender:ethnic_group 4 5.03 5703.2 1716.5
## - parent_educ:practice_sport 10 274.38 5982.6 1716.7
## + parent_educ:lunch_type 5 16.79 5691.4 1717.3
## + parent_educ:wkly_study_hours 10 109.61 5598.6 1717.6
## - parent_marital_status:wkly_study_hours 5 212.67 5920.9 1720.6
## - ethnic_group:writing_score 4 212.01 5920.3 1722.5
## - ethnic_group:parent_educ 20 559.64 6267.9 1724.2
## - ethnic_group:lunch_type 4 233.97 5942.2 1724.7
## - ethnic_group:parent_marital_status 10 452.36 6160.6 1734.0
##
## Step: AIC=1707.16
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:test_prep +
## gender:parent_marital_status + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:wkly_study_hours +
## lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:test_prep 1 2.50 5712.0 1705.4
## - lunch_type:is_first_child 1 2.78 5712.3 1705.5
## - transport_means:math_score 1 2.84 5712.4 1705.5
## - transport_means:wkly_study_hours 2 25.63 5735.1 1705.8
## - test_prep:math_score 1 8.28 5717.8 1706.0
## - gender:parent_marital_status 3 47.94 5757.5 1706.1
## - lunch_type:math_score 1 11.12 5720.6 1706.3
## - gender:lunch_type 1 11.97 5721.5 1706.4
## - ethnic_group:practice_sport 8 149.83 5859.3 1706.5
## - gender:is_first_child 1 14.49 5724.0 1706.7
## - test_prep:transport_means 1 15.10 5724.6 1706.7
## - is_first_child:writing_score 1 16.70 5726.2 1706.9
## - transport_means:writing_score 1 17.00 5726.5 1706.9
## - writing_score:math_score 1 17.08 5726.6 1706.9
## - test_prep:wkly_study_hours 2 37.84 5747.4 1707.1
## - lunch_type:test_prep 1 19.32 5728.8 1707.2
## <none> 5709.5 1707.2
## - lunch_type:practice_sport 2 38.96 5748.5 1707.2
## - test_prep:practice_sport 2 40.26 5749.8 1707.3
## - lunch_type:writing_score 1 26.73 5736.2 1707.9
## - practice_sport:is_first_child 2 46.41 5755.9 1707.9
## - practice_sport:writing_score 2 54.80 5764.3 1708.8
## - gender:math_score 1 37.01 5746.5 1709.0
## - gender:writing_score 1 37.23 5746.7 1709.0
## + lunch_type:transport_means 1 1.27 5708.2 1709.0
## - gender:parent_educ 5 116.89 5826.4 1709.1
## + is_first_child:math_score 1 0.17 5709.3 1709.1
## - is_first_child:transport_means 1 38.68 5748.2 1709.2
## + test_prep:writing_score 1 0.10 5709.4 1709.2
## + gender:transport_means 1 0.00 5709.5 1709.2
## - lunch_type:wkly_study_hours 2 59.93 5769.4 1709.3
## + parent_educ:is_first_child 5 75.35 5634.2 1709.3
## - test_prep:parent_marital_status 2 60.38 5769.9 1709.4
## + ethnic_group:test_prep 4 55.14 5654.4 1709.4
## + parent_marital_status:transport_means 2 15.29 5694.2 1709.6
## + is_first_child:wkly_study_hours 2 11.86 5697.7 1709.9
## - gender:practice_sport 2 66.17 5775.7 1710.0
## - parent_educ:parent_marital_status 14 306.45 6016.0 1710.0
## + practice_sport:transport_means 2 8.80 5700.7 1710.2
## + practice_sport:wkly_study_hours 4 47.07 5662.5 1710.3
## - ethnic_group:transport_means 4 109.95 5819.5 1710.4
## - parent_marital_status:is_first_child 2 70.69 5780.2 1710.4
## - lunch_type:parent_marital_status 3 90.46 5800.0 1710.4
## + parent_educ:transport_means 5 62.67 5646.8 1710.7
## + parent_marital_status:math_score 2 3.31 5706.2 1710.8
## - parent_educ:math_score 5 134.15 5843.7 1710.9
## - parent_educ:test_prep 5 138.88 5848.4 1711.3
## - parent_marital_status:writing_score 3 101.48 5811.0 1711.6
## - wkly_study_hours:math_score 2 81.94 5791.5 1711.6
## - test_prep:is_first_child 1 64.23 5773.7 1711.8
## - practice_sport:math_score 2 86.85 5796.4 1712.1
## + parent_marital_status:practice_sport 4 29.72 5679.8 1712.1
## - gender:wkly_study_hours 2 88.48 5798.0 1712.2
## + parent_educ:writing_score 5 46.11 5663.4 1712.4
## + ethnic_group:is_first_child 4 23.04 5686.5 1712.8
## - wkly_study_hours:writing_score 2 94.11 5803.6 1712.8
## - ethnic_group:wkly_study_hours 8 215.19 5924.7 1713.0
## + ethnic_group:math_score 4 6.61 5702.9 1714.5
## + gender:ethnic_group 4 4.79 5704.7 1714.7
## - parent_educ:practice_sport 10 274.23 5983.7 1714.8
## + parent_educ:lunch_type 5 16.19 5693.3 1715.5
## + parent_educ:wkly_study_hours 10 109.47 5600.0 1715.7
## - parent_marital_status:wkly_study_hours 5 212.84 5922.4 1718.8
## - ethnic_group:writing_score 4 211.84 5921.4 1720.7
## - ethnic_group:parent_educ 20 558.58 6268.1 1722.2
## - ethnic_group:lunch_type 4 236.80 5946.3 1723.1
## - ethnic_group:parent_marital_status 10 451.68 6161.2 1732.1
##
## Step: AIC=1705.42
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:is_first_child + lunch_type:wkly_study_hours +
## lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:is_first_child 1 2.84 5714.9 1703.7
## - transport_means:math_score 1 3.03 5715.0 1703.7
## - test_prep:math_score 1 6.98 5719.0 1704.1
## - transport_means:wkly_study_hours 2 26.80 5738.8 1704.2
## - gender:parent_marital_status 3 46.58 5758.6 1704.2
## - ethnic_group:practice_sport 8 148.56 5860.6 1704.6
## - lunch_type:math_score 1 11.75 5723.8 1704.6
## - gender:lunch_type 1 12.87 5724.9 1704.8
## - test_prep:transport_means 1 14.19 5726.2 1704.9
## - gender:is_first_child 1 15.18 5727.2 1705.0
## - is_first_child:writing_score 1 15.63 5727.6 1705.0
## - transport_means:writing_score 1 15.83 5727.8 1705.0
## - writing_score:math_score 1 16.71 5728.7 1705.1
## - test_prep:wkly_study_hours 2 37.24 5749.3 1705.3
## - lunch_type:test_prep 1 19.35 5731.4 1705.4
## <none> 5712.0 1705.4
## - lunch_type:practice_sport 2 39.44 5751.5 1705.5
## - test_prep:practice_sport 2 40.84 5752.9 1705.6
## - practice_sport:is_first_child 2 45.55 5757.6 1706.1
## - lunch_type:writing_score 1 27.38 5739.4 1706.2
## - gender:math_score 1 34.55 5746.6 1707.0
## - gender:writing_score 1 35.43 5747.4 1707.1
## + gender:test_prep 1 2.50 5709.5 1707.2
## - practice_sport:writing_score 2 56.35 5768.4 1707.2
## + lunch_type:transport_means 1 1.22 5710.8 1707.3
## + test_prep:writing_score 1 1.04 5711.0 1707.3
## + is_first_child:math_score 1 0.15 5711.9 1707.4
## - is_first_child:transport_means 1 38.76 5750.8 1707.4
## + gender:transport_means 1 0.00 5712.0 1707.4
## - lunch_type:wkly_study_hours 2 59.20 5771.2 1707.5
## - test_prep:parent_marital_status 2 61.22 5773.2 1707.7
## + ethnic_group:test_prep 4 54.09 5657.9 1707.8
## + parent_educ:is_first_child 5 72.95 5639.1 1707.8
## + parent_marital_status:transport_means 2 15.13 5696.9 1707.9
## + is_first_child:wkly_study_hours 2 12.52 5699.5 1708.1
## - gender:parent_educ 5 124.76 5836.8 1708.2
## - parent_educ:parent_marital_status 14 306.07 6018.1 1708.2
## - gender:practice_sport 2 68.26 5780.3 1708.4
## - ethnic_group:transport_means 4 108.07 5820.1 1708.5
## + practice_sport:transport_means 2 8.95 5703.1 1708.5
## + practice_sport:wkly_study_hours 4 47.13 5664.9 1708.5
## - lunch_type:parent_marital_status 3 89.56 5801.6 1708.6
## - parent_marital_status:is_first_child 2 70.66 5782.7 1708.7
## + parent_educ:transport_means 5 62.18 5649.8 1709.0
## - parent_educ:math_score 5 133.12 5845.1 1709.0
## + parent_marital_status:math_score 2 3.61 5708.4 1709.0
## - parent_educ:test_prep 5 136.79 5848.8 1709.4
## - wkly_study_hours:math_score 2 81.75 5793.8 1709.8
## - parent_marital_status:writing_score 3 101.48 5813.5 1709.8
## - test_prep:is_first_child 1 63.56 5775.6 1710.0
## + parent_marital_status:practice_sport 4 31.08 5680.9 1710.2
## - gender:wkly_study_hours 2 86.70 5798.7 1710.3
## - practice_sport:math_score 2 88.67 5800.7 1710.5
## + parent_educ:writing_score 5 45.71 5666.3 1710.7
## - ethnic_group:wkly_study_hours 8 213.02 5925.0 1711.0
## - wkly_study_hours:writing_score 2 93.73 5805.7 1711.0
## + ethnic_group:is_first_child 4 22.69 5689.3 1711.1
## + ethnic_group:math_score 4 6.58 5705.4 1712.7
## - parent_educ:practice_sport 10 272.20 5984.2 1712.9
## + gender:ethnic_group 4 4.81 5707.2 1712.9
## + parent_educ:lunch_type 5 16.44 5695.6 1713.7
## + parent_educ:wkly_study_hours 10 109.72 5602.3 1714.0
## - parent_marital_status:wkly_study_hours 5 210.97 5923.0 1716.8
## - ethnic_group:writing_score 4 209.90 5921.9 1718.7
## - ethnic_group:parent_educ 20 556.08 6268.1 1720.2
## - ethnic_group:lunch_type 4 235.35 5947.4 1721.2
## - ethnic_group:parent_marital_status 10 452.96 6165.0 1730.4
##
## Step: AIC=1703.71
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + transport_means:math_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - transport_means:math_score 1 3.31 5718.2 1702.1
## - test_prep:math_score 1 6.49 5721.4 1702.4
## - gender:parent_marital_status 3 45.57 5760.4 1702.4
## - transport_means:wkly_study_hours 2 26.72 5741.6 1702.5
## - lunch_type:math_score 1 11.97 5726.8 1703.0
## - is_first_child:writing_score 1 12.96 5727.8 1703.0
## - gender:is_first_child 1 13.40 5728.3 1703.1
## - ethnic_group:practice_sport 8 151.20 5866.1 1703.1
## - gender:lunch_type 1 13.91 5728.8 1703.2
## - test_prep:transport_means 1 14.91 5729.8 1703.2
## - transport_means:writing_score 1 15.21 5730.1 1703.3
## - test_prep:wkly_study_hours 2 35.26 5750.1 1703.3
## - writing_score:math_score 1 17.45 5732.3 1703.5
## - lunch_type:practice_sport 2 36.95 5751.8 1703.5
## - lunch_type:test_prep 1 18.70 5733.6 1703.6
## <none> 5714.9 1703.7
## - test_prep:practice_sport 2 40.94 5755.8 1703.9
## - practice_sport:is_first_child 2 47.23 5762.1 1704.6
## - lunch_type:writing_score 1 28.29 5743.1 1704.6
## - gender:math_score 1 35.40 5750.3 1705.4
## + lunch_type:is_first_child 1 2.84 5712.0 1705.4
## - gender:writing_score 1 36.05 5750.9 1705.4
## + gender:test_prep 1 2.57 5712.3 1705.5
## - practice_sport:writing_score 2 56.41 5771.3 1705.5
## + lunch_type:transport_means 1 1.10 5713.8 1705.6
## + test_prep:writing_score 1 1.05 5713.8 1705.6
## + is_first_child:math_score 1 0.00 5714.9 1705.7
## + gender:transport_means 1 0.00 5714.9 1705.7
## - is_first_child:transport_means 1 39.57 5754.4 1705.8
## - lunch_type:wkly_study_hours 2 59.29 5774.2 1705.8
## + parent_educ:is_first_child 5 75.45 5639.4 1705.9
## + ethnic_group:test_prep 4 55.41 5659.4 1706.0
## - test_prep:parent_marital_status 2 60.96 5775.8 1706.0
## + parent_marital_status:transport_means 2 15.72 5699.1 1706.1
## - gender:parent_educ 5 123.30 5838.2 1706.3
## + is_first_child:wkly_study_hours 2 12.27 5702.6 1706.5
## - parent_educ:parent_marital_status 14 307.98 6022.8 1706.7
## + practice_sport:wkly_study_hours 4 47.96 5666.9 1706.7
## - gender:practice_sport 2 68.50 5783.4 1706.7
## - lunch_type:parent_marital_status 3 88.62 5803.5 1706.8
## + practice_sport:transport_means 2 8.38 5706.5 1706.8
## - ethnic_group:transport_means 4 110.51 5825.4 1707.0
## - parent_marital_status:is_first_child 2 71.22 5786.1 1707.0
## + parent_marital_status:math_score 2 4.22 5710.6 1707.3
## + parent_educ:transport_means 5 60.92 5653.9 1707.4
## - parent_educ:math_score 5 137.35 5852.2 1707.7
## - parent_educ:test_prep 5 139.11 5854.0 1707.9
## - parent_marital_status:writing_score 3 100.18 5815.0 1708.0
## - wkly_study_hours:math_score 2 80.72 5795.6 1708.0
## - test_prep:is_first_child 1 61.15 5776.0 1708.0
## - gender:wkly_study_hours 2 85.99 5800.9 1708.5
## - practice_sport:math_score 2 88.58 5803.4 1708.8
## + parent_marital_status:practice_sport 4 28.12 5686.7 1708.8
## + parent_educ:writing_score 5 45.03 5669.8 1709.0
## - wkly_study_hours:writing_score 2 92.63 5807.5 1709.2
## + ethnic_group:is_first_child 4 23.28 5691.6 1709.3
## - ethnic_group:wkly_study_hours 8 214.37 5929.2 1709.4
## + ethnic_group:math_score 4 6.01 5708.9 1711.1
## - parent_educ:practice_sport 10 271.85 5986.7 1711.1
## + gender:ethnic_group 4 4.25 5710.6 1711.3
## + parent_educ:lunch_type 5 17.81 5697.0 1711.9
## + parent_educ:wkly_study_hours 10 107.72 5607.1 1712.5
## - parent_marital_status:wkly_study_hours 5 213.17 5928.0 1715.3
## - ethnic_group:writing_score 4 209.35 5924.2 1716.9
## - ethnic_group:lunch_type 4 232.72 5947.6 1719.3
## - ethnic_group:parent_educ 20 571.04 6285.9 1719.9
## - ethnic_group:parent_marital_status 10 450.33 6165.2 1728.5
##
## Step: AIC=1702.06
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + test_prep:math_score + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - test_prep:math_score 1 6.45 5724.6 1700.7
## - transport_means:wkly_study_hours 2 26.29 5744.5 1700.8
## - gender:parent_marital_status 3 46.63 5764.8 1700.8
## - lunch_type:math_score 1 12.40 5730.6 1701.3
## - ethnic_group:practice_sport 8 150.61 5868.8 1701.4
## - is_first_child:writing_score 1 13.49 5731.7 1701.5
## - gender:is_first_child 1 14.07 5732.2 1701.5
## - gender:lunch_type 1 14.68 5732.8 1701.6
## - test_prep:wkly_study_hours 2 34.34 5752.5 1701.6
## - test_prep:transport_means 1 16.61 5734.8 1701.8
## - writing_score:math_score 1 16.82 5735.0 1701.8
## - lunch_type:practice_sport 2 37.96 5756.1 1702.0
## - lunch_type:test_prep 1 19.36 5737.5 1702.0
## <none> 5718.2 1702.1
## - test_prep:practice_sport 2 41.77 5759.9 1702.3
## - practice_sport:is_first_child 2 47.31 5765.5 1702.9
## - lunch_type:writing_score 1 29.04 5747.2 1703.0
## + transport_means:math_score 1 3.31 5714.9 1703.7
## + lunch_type:is_first_child 1 3.12 5715.0 1703.7
## + gender:test_prep 1 2.77 5715.4 1703.8
## - gender:math_score 1 36.26 5754.4 1703.8
## + lunch_type:transport_means 1 2.44 5715.7 1703.8
## + gender:transport_means 1 1.83 5716.3 1703.9
## - gender:writing_score 1 37.41 5755.6 1703.9
## + test_prep:writing_score 1 1.24 5716.9 1703.9
## - is_first_child:transport_means 1 37.69 5755.9 1703.9
## + is_first_child:math_score 1 0.01 5718.2 1704.0
## + parent_educ:is_first_child 5 76.24 5641.9 1704.1
## + ethnic_group:test_prep 4 56.41 5661.8 1704.2
## - test_prep:parent_marital_status 2 59.94 5778.1 1704.2
## - practice_sport:writing_score 2 60.20 5778.4 1704.2
## - gender:parent_educ 5 121.03 5839.2 1704.4
## - lunch_type:wkly_study_hours 2 62.71 5780.9 1704.5
## + parent_marital_status:transport_means 2 14.71 5703.5 1704.5
## + is_first_child:wkly_study_hours 2 12.24 5705.9 1704.8
## - lunch_type:parent_marital_status 3 87.22 5805.4 1705.0
## + practice_sport:wkly_study_hours 4 48.44 5669.7 1705.0
## - parent_educ:parent_marital_status 14 308.43 6026.6 1705.0
## - ethnic_group:transport_means 4 108.05 5826.2 1705.1
## - gender:practice_sport 2 69.54 5787.7 1705.2
## + practice_sport:transport_means 2 8.27 5709.9 1705.2
## - parent_marital_status:is_first_child 2 72.87 5791.0 1705.5
## + parent_marital_status:math_score 2 4.53 5713.6 1705.6
## + parent_educ:transport_means 5 61.34 5656.8 1705.7
## - parent_educ:math_score 5 135.34 5853.5 1705.9
## - wkly_study_hours:math_score 2 79.16 5797.3 1706.2
## - test_prep:is_first_child 1 59.72 5777.9 1706.2
## - parent_marital_status:writing_score 3 100.50 5818.7 1706.3
## - parent_educ:test_prep 5 140.46 5858.6 1706.4
## - gender:wkly_study_hours 2 84.07 5802.2 1706.7
## + parent_marital_status:practice_sport 4 28.58 5689.6 1707.1
## - wkly_study_hours:writing_score 2 90.49 5808.7 1707.3
## + parent_educ:writing_score 5 44.80 5673.4 1707.4
## - ethnic_group:wkly_study_hours 8 211.87 5930.0 1707.5
## - practice_sport:math_score 2 93.21 5811.4 1707.6
## + ethnic_group:is_first_child 4 23.24 5694.9 1707.7
## - transport_means:writing_score 1 82.71 5800.9 1708.5
## + ethnic_group:math_score 4 6.00 5712.2 1709.4
## - parent_educ:practice_sport 10 272.14 5990.3 1709.5
## + gender:ethnic_group 4 4.27 5713.9 1709.6
## + parent_educ:lunch_type 5 17.32 5700.8 1710.3
## + parent_educ:wkly_study_hours 10 108.38 5609.8 1710.8
## - parent_marital_status:wkly_study_hours 5 215.58 5933.7 1713.9
## - ethnic_group:writing_score 4 209.62 5927.8 1715.3
## - ethnic_group:lunch_type 4 232.62 5950.8 1717.6
## - ethnic_group:parent_educ 20 579.00 6297.2 1719.0
## - ethnic_group:parent_marital_status 10 454.06 6172.2 1727.1
##
## Step: AIC=1700.72
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:wkly_study_hours +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - transport_means:wkly_study_hours 2 26.51 5751.1 1699.5
## - gender:parent_marital_status 3 46.82 5771.4 1699.5
## - ethnic_group:practice_sport 8 148.04 5872.7 1699.8
## - writing_score:math_score 1 11.44 5736.1 1699.9
## - test_prep:wkly_study_hours 2 31.43 5756.0 1700.0
## - lunch_type:math_score 1 13.40 5738.0 1700.1
## - lunch_type:test_prep 1 13.94 5738.6 1700.2
## - gender:is_first_child 1 14.87 5739.5 1700.2
## - gender:lunch_type 1 14.90 5739.5 1700.2
## - is_first_child:writing_score 1 15.18 5739.8 1700.3
## - test_prep:transport_means 1 15.71 5740.3 1700.3
## - lunch_type:practice_sport 2 37.53 5762.1 1700.6
## <none> 5724.6 1700.7
## - test_prep:practice_sport 2 43.50 5768.1 1701.2
## - lunch_type:writing_score 1 27.72 5752.3 1701.6
## - practice_sport:is_first_child 2 50.17 5774.8 1701.9
## + test_prep:writing_score 1 7.01 5717.6 1702.0
## + test_prep:math_score 1 6.45 5718.2 1702.1
## + transport_means:math_score 1 3.26 5721.4 1702.4
## + ethnic_group:test_prep 4 60.91 5663.7 1702.4
## + lunch_type:transport_means 1 2.74 5721.9 1702.4
## + lunch_type:is_first_child 1 2.61 5722.0 1702.5
## + gender:transport_means 1 1.88 5722.7 1702.5
## + gender:test_prep 1 1.42 5723.2 1702.6
## - is_first_child:transport_means 1 37.83 5762.4 1702.6
## - gender:math_score 1 38.25 5762.9 1702.7
## - practice_sport:writing_score 2 58.01 5782.6 1702.7
## + is_first_child:math_score 1 0.00 5724.6 1702.7
## - gender:parent_educ 5 118.65 5843.3 1702.8
## + parent_educ:is_first_child 5 76.04 5648.6 1702.8
## - gender:writing_score 1 41.03 5765.6 1702.9
## - test_prep:parent_marital_status 2 61.30 5785.9 1703.0
## - lunch_type:wkly_study_hours 2 61.51 5786.1 1703.0
## + parent_marital_status:transport_means 2 15.00 5709.6 1703.2
## + is_first_child:wkly_study_hours 2 13.09 5711.5 1703.4
## - parent_educ:parent_marital_status 14 307.01 6031.6 1703.5
## - ethnic_group:transport_means 4 106.75 5831.4 1703.6
## - gender:practice_sport 2 67.72 5792.3 1703.7
## + practice_sport:wkly_study_hours 4 48.18 5676.4 1703.7
## + practice_sport:transport_means 2 8.89 5715.7 1703.8
## - lunch_type:parent_marital_status 3 90.19 5814.8 1703.9
## - parent_educ:math_score 5 130.18 5854.8 1704.0
## - parent_marital_status:is_first_child 2 72.21 5796.8 1704.1
## + parent_marital_status:math_score 2 4.28 5720.3 1704.3
## + parent_educ:transport_means 5 60.74 5663.9 1704.4
## - wkly_study_hours:math_score 2 77.63 5802.2 1704.7
## - parent_marital_status:writing_score 3 99.07 5823.7 1704.8
## - parent_educ:test_prep 5 139.69 5864.3 1704.9
## - test_prep:is_first_child 1 63.06 5787.7 1705.2
## - gender:wkly_study_hours 2 83.46 5808.1 1705.3
## + parent_marital_status:practice_sport 4 28.55 5696.1 1705.8
## - wkly_study_hours:writing_score 2 89.79 5814.4 1705.9
## + parent_educ:writing_score 5 45.60 5679.0 1706.0
## - ethnic_group:wkly_study_hours 8 210.43 5935.0 1706.0
## - practice_sport:math_score 2 91.36 5816.0 1706.1
## + ethnic_group:is_first_child 4 23.06 5701.6 1706.3
## - transport_means:writing_score 1 78.46 5803.1 1706.8
## + ethnic_group:math_score 4 6.60 5718.0 1708.0
## + gender:ethnic_group 4 4.08 5720.5 1708.3
## - parent_educ:practice_sport 10 275.07 5999.7 1708.4
## + parent_educ:lunch_type 5 19.25 5705.4 1708.7
## + parent_educ:wkly_study_hours 10 107.75 5616.9 1709.5
## - parent_marital_status:wkly_study_hours 5 215.63 5940.2 1712.5
## - ethnic_group:writing_score 4 208.06 5932.7 1713.8
## - ethnic_group:lunch_type 4 229.78 5954.4 1715.9
## - ethnic_group:parent_educ 20 577.42 6302.0 1717.4
## - ethnic_group:parent_marital_status 10 453.22 6177.8 1725.7
##
## Step: AIC=1699.45
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:parent_marital_status +
## gender:practice_sport + gender:is_first_child + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:parent_marital_status 3 45.91 5797.0 1698.1
## - test_prep:wkly_study_hours 2 28.23 5779.4 1698.3
## - writing_score:math_score 1 10.25 5761.4 1698.5
## - lunch_type:test_prep 1 11.52 5762.6 1698.6
## - ethnic_group:practice_sport 8 151.27 5902.4 1698.8
## - lunch_type:practice_sport 2 34.43 5785.6 1699.0
## - test_prep:transport_means 1 15.21 5766.3 1699.0
## - is_first_child:writing_score 1 15.86 5767.0 1699.1
## - lunch_type:math_score 1 16.31 5767.4 1699.1
## - gender:lunch_type 1 16.32 5767.4 1699.1
## - gender:is_first_child 1 17.15 5768.3 1699.2
## <none> 5751.1 1699.5
## - test_prep:practice_sport 2 45.38 5796.5 1700.1
## + test_prep:writing_score 1 8.38 5742.7 1700.6
## - practice_sport:is_first_child 2 50.93 5802.0 1700.7
## - lunch_type:writing_score 1 31.64 5782.8 1700.7
## + transport_means:wkly_study_hours 2 26.51 5724.6 1700.7
## + test_prep:math_score 1 6.67 5744.5 1700.8
## + parent_educ:is_first_child 5 81.02 5670.1 1701.1
## - gender:math_score 1 36.05 5787.2 1701.1
## + transport_means:math_score 1 2.82 5748.3 1701.2
## + lunch_type:is_first_child 1 2.46 5748.7 1701.2
## + gender:test_prep 1 2.28 5748.8 1701.2
## + gender:transport_means 1 1.88 5749.2 1701.2
## + lunch_type:transport_means 1 1.54 5749.6 1701.3
## - gender:parent_educ 5 116.77 5867.9 1701.3
## + is_first_child:math_score 1 0.02 5751.1 1701.4
## - is_first_child:transport_means 1 39.56 5790.7 1701.5
## - test_prep:parent_marital_status 2 59.93 5811.1 1701.6
## - gender:writing_score 1 40.60 5791.7 1701.6
## - practice_sport:writing_score 2 60.88 5812.0 1701.7
## - lunch_type:wkly_study_hours 2 61.20 5812.3 1701.7
## + parent_marital_status:transport_means 2 15.62 5735.5 1701.8
## + is_first_child:wkly_study_hours 2 15.31 5735.8 1701.9
## + ethnic_group:test_prep 4 53.67 5697.5 1701.9
## - ethnic_group:transport_means 4 104.97 5856.1 1702.1
## - parent_marital_status:is_first_child 2 68.06 5819.2 1702.4
## - gender:practice_sport 2 68.88 5820.0 1702.5
## + practice_sport:transport_means 2 8.61 5742.5 1702.6
## - parent_educ:math_score 5 130.96 5882.1 1702.7
## - wkly_study_hours:math_score 2 72.92 5824.0 1702.9
## + parent_marital_status:math_score 2 5.34 5745.8 1702.9
## + practice_sport:wkly_study_hours 4 43.63 5707.5 1703.0
## + parent_educ:transport_means 5 60.49 5690.6 1703.2
## - parent_educ:test_prep 5 138.21 5889.3 1703.5
## - gender:wkly_study_hours 2 78.82 5829.9 1703.5
## - parent_educ:parent_marital_status 14 321.88 6073.0 1703.6
## - test_prep:is_first_child 1 60.63 5811.8 1703.6
## - lunch_type:parent_marital_status 3 100.91 5852.0 1703.7
## - ethnic_group:wkly_study_hours 8 206.24 5957.4 1704.2
## - wkly_study_hours:writing_score 2 87.15 5838.3 1704.3
## + parent_marital_status:practice_sport 4 28.89 5722.2 1704.5
## - parent_marital_status:writing_score 3 109.41 5860.5 1704.6
## - transport_means:writing_score 1 72.46 5823.6 1704.8
## + ethnic_group:is_first_child 4 20.69 5730.4 1705.3
## - parent_educ:practice_sport 10 257.90 6009.0 1705.3
## + parent_educ:writing_score 5 39.90 5711.2 1705.3
## - practice_sport:math_score 2 97.42 5848.5 1705.4
## + ethnic_group:math_score 4 5.75 5745.4 1706.9
## + gender:ethnic_group 4 2.79 5748.3 1707.2
## + parent_educ:lunch_type 5 19.36 5731.8 1707.5
## + parent_educ:wkly_study_hours 10 111.32 5639.8 1707.9
## - parent_marital_status:wkly_study_hours 5 214.49 5965.6 1711.0
## - ethnic_group:writing_score 4 211.92 5963.0 1712.8
## - ethnic_group:lunch_type 4 222.08 5973.2 1713.8
## - ethnic_group:parent_educ 20 561.71 6312.8 1714.4
## - ethnic_group:parent_marital_status 10 456.45 6207.6 1724.5
##
## Step: AIC=1698.14
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## test_prep:wkly_study_hours + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## is_first_child:writing_score + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - test_prep:wkly_study_hours 2 23.24 5820.3 1696.5
## - lunch_type:practice_sport 2 30.42 5827.5 1697.2
## - lunch_type:math_score 1 13.75 5810.8 1697.5
## - test_prep:transport_means 1 15.50 5812.5 1697.7
## - gender:is_first_child 1 15.59 5812.6 1697.7
## - lunch_type:test_prep 1 15.98 5813.0 1697.8
## - writing_score:math_score 1 16.00 5813.0 1697.8
## - is_first_child:writing_score 1 16.20 5813.2 1697.8
## - gender:lunch_type 1 16.43 5813.5 1697.8
## <none> 5797.0 1698.1
## - ethnic_group:practice_sport 8 162.19 5959.2 1698.4
## - test_prep:practice_sport 2 44.37 5841.4 1698.6
## - practice_sport:is_first_child 2 46.17 5843.2 1698.8
## - lunch_type:writing_score 1 30.25 5827.3 1699.2
## + test_prep:writing_score 1 8.14 5788.9 1699.3
## + test_prep:math_score 1 6.87 5790.2 1699.4
## + gender:parent_marital_status 3 45.91 5751.1 1699.5
## + parent_educ:is_first_child 5 84.41 5712.6 1699.5
## + transport_means:wkly_study_hours 2 25.60 5771.4 1699.5
## + transport_means:math_score 1 3.73 5793.3 1699.8
## - lunch_type:wkly_study_hours 2 56.40 5853.4 1699.8
## + gender:transport_means 1 2.12 5794.9 1699.9
## + lunch_type:is_first_child 1 1.60 5795.4 1700.0
## + lunch_type:transport_means 1 1.14 5795.9 1700.0
## - test_prep:parent_marital_status 2 58.17 5855.2 1700.0
## + gender:test_prep 1 1.03 5796.0 1700.0
## - is_first_child:transport_means 1 39.00 5836.0 1700.1
## + is_first_child:math_score 1 0.00 5797.0 1700.1
## - practice_sport:writing_score 2 59.43 5856.5 1700.2
## - gender:writing_score 1 42.16 5839.2 1700.4
## + ethnic_group:test_prep 4 55.64 5741.4 1700.5
## - gender:math_score 1 42.87 5839.9 1700.5
## - ethnic_group:transport_means 4 103.53 5900.6 1700.6
## - parent_educ:test_prep 5 123.58 5920.6 1700.6
## + is_first_child:wkly_study_hours 2 14.62 5782.4 1700.7
## - gender:parent_educ 5 125.85 5922.9 1700.8
## - gender:practice_sport 2 67.78 5864.8 1701.0
## - parent_marital_status:is_first_child 2 68.32 5865.4 1701.0
## - lunch_type:parent_marital_status 3 88.99 5886.0 1701.1
## - wkly_study_hours:math_score 2 70.85 5867.9 1701.3
## + practice_sport:transport_means 2 8.16 5788.9 1701.3
## + parent_marital_status:transport_means 3 24.28 5772.8 1701.7
## + practice_sport:wkly_study_hours 4 41.66 5755.4 1701.9
## - parent_marital_status:writing_score 3 97.04 5894.1 1701.9
## - parent_educ:math_score 5 138.24 5935.3 1702.0
## + parent_educ:transport_means 5 58.99 5738.0 1702.1
## - test_prep:is_first_child 1 61.40 5858.4 1702.3
## + parent_marital_status:math_score 3 17.36 5779.7 1702.4
## - gender:wkly_study_hours 2 81.91 5878.9 1702.4
## - ethnic_group:wkly_study_hours 8 205.57 6002.6 1702.7
## - wkly_study_hours:writing_score 2 85.84 5882.9 1702.8
## + parent_marital_status:practice_sport 4 32.32 5764.7 1702.8
## + parent_educ:writing_score 5 43.92 5753.1 1703.7
## - parent_educ:practice_sport 10 257.67 6054.7 1703.8
## - practice_sport:math_score 2 95.86 5892.9 1703.8
## - transport_means:writing_score 1 80.24 5877.3 1704.2
## - parent_educ:parent_marital_status 14 345.06 6142.1 1704.2
## + ethnic_group:is_first_child 4 18.37 5778.7 1704.3
## + ethnic_group:math_score 4 2.96 5794.1 1705.8
## + gender:ethnic_group 4 1.99 5795.0 1705.9
## + parent_educ:lunch_type 5 18.66 5778.4 1706.2
## + parent_educ:wkly_study_hours 10 108.48 5688.6 1707.0
## - parent_marital_status:wkly_study_hours 5 224.56 6021.6 1710.6
## - ethnic_group:writing_score 4 212.86 6009.9 1711.4
## - ethnic_group:parent_educ 20 548.79 6345.8 1711.5
## - ethnic_group:lunch_type 4 215.91 6012.9 1711.7
## - ethnic_group:parent_marital_status 10 454.57 6251.6 1722.7
##
## Step: AIC=1696.5
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:practice_sport +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:practice_sport 2 32.13 5852.4 1695.8
## - lunch_type:math_score 1 13.63 5833.9 1695.9
## - gender:is_first_child 1 15.91 5836.2 1696.1
## - is_first_child:writing_score 1 16.39 5836.7 1696.2
## - test_prep:transport_means 1 16.50 5836.8 1696.2
## - gender:lunch_type 1 17.25 5837.5 1696.2
## - writing_score:math_score 1 17.67 5837.9 1696.3
## <none> 5820.3 1696.5
## - lunch_type:test_prep 1 20.30 5840.6 1696.5
## - test_prep:practice_sport 2 43.98 5864.2 1696.9
## - practice_sport:is_first_child 2 45.32 5865.6 1697.1
## - lunch_type:writing_score 1 32.24 5852.5 1697.8
## + test_prep:writing_score 1 5.63 5814.6 1697.9
## + test_prep:math_score 1 4.06 5816.2 1698.1
## + test_prep:wkly_study_hours 2 23.24 5797.0 1698.1
## - ethnic_group:practice_sport 8 177.07 5997.3 1698.2
## + transport_means:math_score 1 3.01 5817.3 1698.2
## + transport_means:wkly_study_hours 2 22.59 5797.7 1698.2
## + parent_educ:is_first_child 5 80.40 5739.9 1698.3
## + gender:transport_means 1 1.67 5818.6 1698.3
## + gender:parent_marital_status 3 40.92 5779.4 1698.3
## - wkly_study_hours:math_score 2 58.43 5878.7 1698.4
## + gender:test_prep 1 0.91 5819.4 1698.4
## + lunch_type:is_first_child 1 0.44 5819.8 1698.5
## + lunch_type:transport_means 1 0.42 5819.9 1698.5
## + is_first_child:math_score 1 0.34 5819.9 1698.5
## - practice_sport:writing_score 2 59.32 5879.6 1698.5
## - gender:parent_educ 5 119.63 5939.9 1698.5
## - lunch_type:wkly_study_hours 2 59.64 5879.9 1698.5
## - gender:writing_score 1 41.77 5862.0 1698.7
## - is_first_child:transport_means 1 41.94 5862.2 1698.7
## - parent_educ:test_prep 5 122.04 5942.3 1698.7
## - gender:math_score 1 43.29 5863.6 1698.9
## - parent_marital_status:is_first_child 2 64.43 5884.7 1699.0
## - test_prep:parent_marital_status 2 66.39 5886.7 1699.2
## - gender:practice_sport 2 67.26 5887.5 1699.3
## + is_first_child:wkly_study_hours 2 10.65 5809.6 1699.4
## - ethnic_group:transport_means 4 108.74 5929.0 1699.4
## + ethnic_group:test_prep 4 49.62 5770.7 1699.5
## - lunch_type:parent_marital_status 3 90.26 5910.5 1699.6
## + practice_sport:transport_means 2 8.04 5812.2 1699.7
## - wkly_study_hours:writing_score 2 73.78 5894.1 1699.9
## + parent_marital_status:transport_means 3 25.26 5795.0 1699.9
## + practice_sport:wkly_study_hours 4 42.66 5777.6 1700.2
## - gender:wkly_study_hours 2 76.66 5896.9 1700.2
## - parent_marital_status:writing_score 3 96.88 5917.2 1700.2
## + parent_educ:transport_means 5 60.08 5760.2 1700.4
## - test_prep:is_first_child 1 61.41 5881.7 1700.7
## + parent_marital_status:practice_sport 4 36.20 5784.1 1700.8
## + parent_marital_status:math_score 3 13.35 5806.9 1701.1
## - parent_educ:math_score 5 146.86 5967.1 1701.2
## - ethnic_group:wkly_study_hours 8 211.83 6032.1 1701.6
## + parent_educ:writing_score 5 43.52 5776.8 1702.1
## - practice_sport:math_score 2 96.57 5916.8 1702.2
## - parent_educ:practice_sport 10 261.93 6082.2 1702.5
## - parent_educ:parent_marital_status 14 346.60 6166.9 1702.6
## + ethnic_group:is_first_child 4 14.92 5805.4 1703.0
## - transport_means:writing_score 1 87.51 5907.8 1703.3
## + ethnic_group:math_score 4 3.24 5817.0 1704.2
## + gender:ethnic_group 4 2.93 5817.3 1704.2
## + parent_educ:lunch_type 5 19.29 5801.0 1704.5
## + parent_educ:wkly_study_hours 10 108.15 5712.1 1705.4
## - parent_marital_status:wkly_study_hours 5 225.81 6046.1 1709.0
## - ethnic_group:lunch_type 4 205.74 6026.0 1709.0
## - ethnic_group:writing_score 4 211.28 6031.6 1709.5
## - ethnic_group:parent_educ 20 565.38 6385.7 1711.2
## - ethnic_group:parent_marital_status 10 466.66 6286.9 1722.0
##
## Step: AIC=1695.75
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:wkly_study_hours +
## lunch_type:writing_score + lunch_type:math_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:math_score 1 10.89 5863.3 1694.8
## - gender:is_first_child 1 13.47 5865.9 1695.1
## - gender:lunch_type 1 14.22 5866.6 1695.2
## - test_prep:transport_means 1 14.77 5867.2 1695.2
## - is_first_child:writing_score 1 16.11 5868.5 1695.4
## - writing_score:math_score 1 17.08 5869.5 1695.5
## <none> 5852.4 1695.8
## - test_prep:practice_sport 2 40.04 5892.4 1695.8
## - lunch_type:test_prep 1 22.00 5874.4 1696.0
## - practice_sport:is_first_child 2 44.68 5897.1 1696.2
## + lunch_type:practice_sport 2 32.13 5820.3 1696.5
## - lunch_type:writing_score 1 28.08 5880.5 1696.6
## - gender:writing_score 1 34.35 5886.8 1697.2
## + test_prep:wkly_study_hours 2 24.95 5827.5 1697.2
## + test_prep:writing_score 1 4.85 5847.6 1697.3
## - gender:math_score 1 35.40 5887.8 1697.3
## + test_prep:math_score 1 3.69 5848.7 1697.4
## + transport_means:math_score 1 3.69 5848.7 1697.4
## - wkly_study_hours:math_score 2 57.91 5910.3 1697.6
## + gender:transport_means 1 1.85 5850.6 1697.6
## + gender:test_prep 1 1.16 5851.2 1697.6
## + is_first_child:math_score 1 0.67 5851.7 1697.7
## + lunch_type:is_first_child 1 0.09 5852.3 1697.7
## + lunch_type:transport_means 1 0.08 5852.3 1697.7
## + transport_means:wkly_study_hours 2 19.59 5832.8 1697.8
## - lunch_type:wkly_study_hours 2 61.01 5913.4 1697.9
## - gender:parent_educ 5 121.71 5974.1 1697.9
## + gender:parent_marital_status 3 37.02 5815.4 1698.0
## - test_prep:parent_marital_status 2 62.69 5915.1 1698.0
## + is_first_child:wkly_study_hours 2 15.42 5837.0 1698.2
## + parent_educ:is_first_child 5 74.18 5778.2 1698.2
## - practice_sport:writing_score 2 64.73 5917.1 1698.2
## - parent_marital_status:is_first_child 2 65.24 5917.6 1698.3
## + ethnic_group:test_prep 4 50.54 5801.9 1698.6
## - lunch_type:parent_marital_status 3 89.05 5941.5 1698.7
## - gender:practice_sport 2 69.40 5921.8 1698.7
## - is_first_child:transport_means 1 50.70 5903.1 1698.8
## - ethnic_group:transport_means 4 111.10 5963.5 1698.8
## + practice_sport:transport_means 2 8.66 5843.7 1698.9
## - wkly_study_hours:writing_score 2 72.56 5925.0 1699.0
## + parent_educ:transport_means 5 66.34 5786.1 1699.0
## - parent_marital_status:writing_score 3 94.90 5947.3 1699.2
## + parent_marital_status:transport_means 3 23.44 5829.0 1699.4
## - parent_educ:test_prep 5 137.38 5989.8 1699.4
## - ethnic_group:practice_sport 8 199.43 6051.8 1699.5
## + parent_marital_status:practice_sport 4 38.57 5813.8 1699.8
## - test_prep:is_first_child 1 61.11 5913.5 1699.9
## + practice_sport:wkly_study_hours 4 37.71 5814.7 1699.9
## - gender:wkly_study_hours 2 82.06 5934.5 1700.0
## - ethnic_group:wkly_study_hours 8 208.02 6060.4 1700.3
## - parent_educ:math_score 5 147.20 5999.6 1700.4
## + parent_marital_status:math_score 3 12.05 5840.3 1700.5
## + parent_educ:writing_score 5 45.09 5807.3 1701.2
## - practice_sport:math_score 2 100.45 5952.8 1701.8
## + ethnic_group:is_first_child 4 15.73 5836.7 1702.2
## - transport_means:writing_score 1 85.85 5938.2 1702.3
## - parent_educ:parent_marital_status 14 360.09 6212.5 1703.0
## + gender:ethnic_group 4 4.20 5848.2 1703.3
## + ethnic_group:math_score 4 2.94 5849.5 1703.5
## - parent_educ:practice_sport 10 283.48 6135.9 1703.7
## + parent_educ:lunch_type 5 20.52 5831.9 1703.7
## + parent_educ:wkly_study_hours 10 112.06 5740.3 1704.3
## - ethnic_group:lunch_type 4 198.79 6051.2 1707.5
## - parent_marital_status:wkly_study_hours 5 226.28 6078.7 1708.1
## - ethnic_group:writing_score 4 214.10 6066.5 1709.0
## - ethnic_group:parent_educ 20 573.66 6426.1 1710.9
## - ethnic_group:parent_marital_status 10 470.73 6323.1 1721.4
##
## Step: AIC=1694.84
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:lunch_type + gender:practice_sport +
## gender:is_first_child + gender:wkly_study_hours + gender:writing_score +
## gender:math_score + ethnic_group:parent_educ + ethnic_group:lunch_type +
## ethnic_group:parent_marital_status + ethnic_group:practice_sport +
## ethnic_group:transport_means + ethnic_group:wkly_study_hours +
## ethnic_group:writing_score + parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:wkly_study_hours +
## lunch_type:writing_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:lunch_type 1 3.91 5867.2 1693.2
## - gender:is_first_child 1 11.31 5874.6 1694.0
## - test_prep:transport_means 1 13.99 5877.3 1694.2
## - is_first_child:writing_score 1 14.42 5877.7 1694.3
## - lunch_type:test_prep 1 15.73 5879.0 1694.4
## - test_prep:practice_sport 2 37.88 5901.2 1694.6
## <none> 5863.3 1694.8
## - writing_score:math_score 1 24.14 5887.4 1695.3
## - practice_sport:is_first_child 2 44.92 5908.2 1695.3
## - lunch_type:writing_score 1 25.39 5888.7 1695.4
## + lunch_type:math_score 1 10.89 5852.4 1695.8
## + lunch_type:practice_sport 2 29.38 5833.9 1695.9
## - gender:writing_score 1 33.76 5897.0 1696.2
## + test_prep:writing_score 1 5.42 5857.9 1696.3
## + test_prep:wkly_study_hours 2 24.75 5838.5 1696.3
## - gender:math_score 1 34.97 5898.3 1696.3
## + test_prep:math_score 1 4.36 5858.9 1696.4
## - wkly_study_hours:math_score 2 55.66 5918.9 1696.4
## + transport_means:math_score 1 4.06 5859.2 1696.4
## - gender:parent_educ 5 117.77 5981.1 1696.6
## + transport_means:wkly_study_hours 2 21.71 5841.6 1696.7
## + gender:transport_means 1 1.82 5861.5 1696.7
## + gender:test_prep 1 1.55 5861.7 1696.7
## + lunch_type:transport_means 1 0.34 5862.9 1696.8
## + is_first_child:math_score 1 0.33 5863.0 1696.8
## + lunch_type:is_first_child 1 0.04 5863.3 1696.8
## - lunch_type:wkly_study_hours 2 62.36 5925.6 1697.1
## - parent_marital_status:is_first_child 2 62.37 5925.7 1697.1
## - lunch_type:parent_marital_status 3 83.61 5946.9 1697.2
## - test_prep:parent_marital_status 2 63.55 5926.8 1697.2
## + parent_educ:is_first_child 5 74.96 5788.3 1697.2
## + is_first_child:wkly_study_hours 2 15.64 5847.7 1697.3
## + gender:parent_marital_status 3 35.13 5828.2 1697.3
## - practice_sport:writing_score 2 66.22 5929.5 1697.5
## - ethnic_group:transport_means 4 107.86 5971.1 1697.6
## - gender:practice_sport 2 68.26 5931.5 1697.7
## - parent_marital_status:writing_score 3 89.03 5952.3 1697.7
## - wkly_study_hours:writing_score 2 69.70 5933.0 1697.8
## + practice_sport:transport_means 2 8.75 5854.5 1698.0
## + ethnic_group:test_prep 4 46.91 5816.4 1698.1
## - is_first_child:transport_means 1 54.77 5918.1 1698.3
## + parent_educ:transport_means 5 63.26 5800.0 1698.4
## - parent_educ:test_prep 5 137.76 6001.1 1698.5
## + parent_marital_status:transport_means 3 20.74 5842.6 1698.8
## - gender:wkly_study_hours 2 79.24 5942.5 1698.8
## + parent_marital_status:practice_sport 4 40.06 5823.2 1698.8
## - ethnic_group:practice_sport 8 201.81 6065.1 1698.8
## - test_prep:is_first_child 1 60.77 5924.1 1698.9
## + practice_sport:wkly_study_hours 4 37.86 5825.4 1699.0
## - ethnic_group:wkly_study_hours 8 208.79 6072.1 1699.5
## - parent_educ:math_score 5 148.49 6011.8 1699.6
## + parent_marital_status:math_score 3 11.56 5851.7 1699.7
## + parent_educ:writing_score 5 43.34 5819.9 1700.5
## - practice_sport:math_score 2 101.61 5964.9 1701.0
## - transport_means:writing_score 1 84.70 5948.0 1701.3
## + ethnic_group:is_first_child 4 14.88 5848.4 1701.3
## - parent_educ:parent_marital_status 14 353.23 6216.5 1701.4
## + gender:ethnic_group 4 4.60 5858.7 1702.4
## + ethnic_group:math_score 4 2.73 5860.6 1702.6
## + parent_educ:lunch_type 5 20.73 5842.6 1702.8
## - parent_educ:practice_sport 10 284.88 6148.2 1702.8
## + parent_educ:wkly_study_hours 10 108.79 5754.5 1703.8
## - ethnic_group:lunch_type 4 188.67 6052.0 1705.5
## - parent_marital_status:wkly_study_hours 5 220.74 6084.0 1706.7
## - ethnic_group:writing_score 4 212.27 6075.6 1707.8
## - ethnic_group:parent_educ 20 572.96 6436.2 1709.8
## - ethnic_group:parent_marital_status 10 464.08 6327.4 1719.8
##
## Step: AIC=1693.24
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:is_first_child +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:wkly_study_hours +
## lunch_type:writing_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - gender:is_first_child 1 11.12 5878.3 1692.3
## - test_prep:transport_means 1 13.28 5880.5 1692.6
## - lunch_type:test_prep 1 13.98 5881.2 1692.6
## - is_first_child:writing_score 1 14.12 5881.3 1692.7
## - test_prep:practice_sport 2 36.93 5904.1 1692.9
## <none> 5867.2 1693.2
## - writing_score:math_score 1 21.18 5888.4 1693.4
## - lunch_type:writing_score 1 21.49 5888.7 1693.4
## - practice_sport:is_first_child 2 42.85 5910.1 1693.5
## + lunch_type:practice_sport 2 28.82 5838.4 1694.3
## - gender:math_score 1 31.18 5898.4 1694.4
## - gender:writing_score 1 31.30 5898.5 1694.4
## + test_prep:wkly_study_hours 2 25.36 5841.8 1694.7
## + test_prep:writing_score 1 5.03 5862.2 1694.7
## + transport_means:math_score 1 4.44 5862.8 1694.8
## + test_prep:math_score 1 3.98 5863.2 1694.8
## + gender:lunch_type 1 3.91 5863.3 1694.8
## + gender:transport_means 1 1.99 5865.2 1695.0
## - gender:parent_educ 5 118.59 5985.8 1695.0
## + gender:test_prep 1 1.85 5865.3 1695.0
## + transport_means:wkly_study_hours 2 21.17 5846.0 1695.1
## + lunch_type:math_score 1 0.57 5866.6 1695.2
## + lunch_type:transport_means 1 0.43 5866.8 1695.2
## + is_first_child:math_score 1 0.28 5866.9 1695.2
## + lunch_type:is_first_child 1 0.00 5867.2 1695.2
## - wkly_study_hours:math_score 2 60.56 5927.8 1695.3
## - parent_marital_status:is_first_child 2 61.80 5929.0 1695.4
## - test_prep:parent_marital_status 2 62.34 5929.5 1695.5
## + parent_educ:is_first_child 5 76.68 5790.5 1695.5
## + gender:parent_marital_status 3 36.43 5830.8 1695.6
## - lunch_type:wkly_study_hours 2 63.76 5931.0 1695.6
## + is_first_child:wkly_study_hours 2 14.84 5852.4 1695.7
## - lunch_type:parent_marital_status 3 85.63 5952.8 1695.8
## - ethnic_group:transport_means 4 107.07 5974.3 1695.9
## - practice_sport:writing_score 2 68.41 5935.6 1696.1
## - gender:practice_sport 2 68.63 5935.8 1696.1
## - parent_marital_status:writing_score 3 90.06 5957.3 1696.2
## + practice_sport:transport_means 2 8.69 5858.5 1696.4
## - wkly_study_hours:writing_score 2 73.28 5940.5 1696.6
## + ethnic_group:test_prep 4 45.94 5821.3 1696.6
## - ethnic_group:practice_sport 8 199.26 6066.5 1696.9
## - parent_educ:test_prep 5 138.12 6005.3 1697.0
## - is_first_child:transport_means 1 57.29 5924.5 1697.0
## + parent_marital_status:transport_means 3 21.29 5845.9 1697.1
## - test_prep:is_first_child 1 58.80 5926.0 1697.1
## - gender:wkly_study_hours 2 79.39 5946.6 1697.2
## + parent_marital_status:practice_sport 4 40.10 5827.1 1697.2
## + parent_educ:transport_means 5 59.42 5807.8 1697.2
## + practice_sport:wkly_study_hours 4 38.24 5829.0 1697.4
## - ethnic_group:wkly_study_hours 8 206.65 6073.9 1697.7
## - parent_educ:math_score 5 146.33 6013.5 1697.8
## + parent_marital_status:math_score 3 13.17 5854.0 1697.9
## + parent_educ:writing_score 5 41.70 5825.5 1699.0
## - transport_means:writing_score 1 83.51 5950.7 1699.6
## - practice_sport:math_score 2 103.74 5970.9 1699.6
## + ethnic_group:is_first_child 4 14.57 5852.6 1699.8
## - parent_educ:parent_marital_status 14 354.13 6221.3 1699.8
## + gender:ethnic_group 4 4.52 5862.7 1700.8
## + ethnic_group:math_score 4 2.87 5864.3 1701.0
## + parent_educ:lunch_type 5 20.62 5846.6 1701.2
## - parent_educ:practice_sport 10 286.45 6153.6 1701.4
## + parent_educ:wkly_study_hours 10 109.22 5758.0 1702.2
## - ethnic_group:lunch_type 4 190.93 6058.1 1704.1
## - parent_marital_status:wkly_study_hours 5 218.94 6086.1 1704.8
## - ethnic_group:writing_score 4 219.50 6086.7 1706.9
## - ethnic_group:parent_educ 20 569.20 6436.4 1707.9
## - ethnic_group:parent_marital_status 10 462.11 6329.3 1718.0
##
## Step: AIC=1692.35
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:wkly_study_hours +
## lunch_type:writing_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + is_first_child:writing_score +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - is_first_child:writing_score 1 8.43 5886.7 1691.2
## - lunch_type:test_prep 1 12.58 5890.9 1691.6
## - test_prep:transport_means 1 13.56 5891.9 1691.7
## - test_prep:practice_sport 2 37.74 5916.1 1692.1
## <none> 5878.3 1692.3
## - lunch_type:writing_score 1 20.95 5899.3 1692.5
## - writing_score:math_score 1 21.44 5899.8 1692.5
## - practice_sport:is_first_child 2 43.80 5922.1 1692.7
## + gender:is_first_child 1 11.12 5867.2 1693.2
## - gender:writing_score 1 30.05 5908.4 1693.4
## - gender:math_score 1 31.06 5909.4 1693.5
## + is_first_child:math_score 1 8.27 5870.1 1693.5
## + lunch_type:practice_sport 2 27.04 5851.3 1693.6
## + test_prep:writing_score 1 6.34 5872.0 1693.7
## + test_prep:wkly_study_hours 2 25.56 5852.8 1693.8
## + transport_means:math_score 1 5.10 5873.2 1693.8
## + test_prep:math_score 1 4.56 5873.8 1693.9
## + gender:lunch_type 1 3.72 5874.6 1694.0
## - parent_marital_status:is_first_child 2 56.92 5935.2 1694.0
## + transport_means:wkly_study_hours 2 22.52 5855.8 1694.1
## - gender:parent_educ 5 118.29 5996.6 1694.1
## + gender:test_prep 1 2.29 5876.0 1694.1
## + parent_educ:is_first_child 5 81.35 5797.0 1694.1
## + gender:transport_means 1 2.10 5876.2 1694.1
## + lunch_type:transport_means 1 0.79 5877.5 1694.3
## - wkly_study_hours:math_score 2 59.59 5937.9 1694.3
## + lunch_type:is_first_child 1 0.36 5878.0 1694.3
## + lunch_type:math_score 1 0.33 5878.0 1694.3
## - test_prep:parent_marital_status 2 63.10 5941.4 1694.7
## - lunch_type:wkly_study_hours 2 64.38 5942.7 1694.8
## + gender:parent_marital_status 3 35.29 5843.0 1694.8
## - ethnic_group:transport_means 4 105.33 5983.7 1694.8
## - practice_sport:writing_score 2 65.75 5944.1 1694.9
## - lunch_type:parent_marital_status 3 86.19 5964.5 1694.9
## - gender:practice_sport 2 66.13 5944.5 1695.0
## + is_first_child:wkly_study_hours 2 13.39 5864.9 1695.0
## - parent_marital_status:writing_score 3 89.81 5968.1 1695.3
## - wkly_study_hours:writing_score 2 71.99 5950.3 1695.5
## - test_prep:is_first_child 1 52.34 5930.7 1695.6
## + ethnic_group:test_prep 4 46.82 5831.5 1695.6
## - ethnic_group:practice_sport 8 195.30 6073.6 1695.6
## + practice_sport:transport_means 2 7.06 5871.3 1695.6
## - parent_educ:test_prep 5 134.57 6012.9 1695.7
## + parent_marital_status:transport_means 3 20.89 5857.4 1696.2
## + parent_marital_status:practice_sport 4 40.70 5837.6 1696.2
## - gender:wkly_study_hours 2 79.30 5957.6 1696.3
## + parent_educ:transport_means 5 59.70 5818.6 1696.3
## - is_first_child:transport_means 1 60.02 5938.3 1696.3
## - ethnic_group:wkly_study_hours 8 203.40 6081.7 1696.4
## + practice_sport:wkly_study_hours 4 39.02 5839.3 1696.4
## + parent_marital_status:math_score 3 11.88 5866.4 1697.2
## - parent_educ:math_score 5 152.54 6030.9 1697.5
## + parent_educ:writing_score 5 43.02 5835.3 1698.0
## - practice_sport:math_score 2 101.53 5979.8 1698.5
## - transport_means:writing_score 1 84.99 5963.3 1698.8
## - parent_educ:parent_marital_status 14 354.15 6232.5 1698.9
## + ethnic_group:is_first_child 4 13.19 5865.1 1699.0
## + gender:ethnic_group 4 5.86 5872.5 1699.8
## + ethnic_group:math_score 4 2.38 5875.9 1700.1
## + parent_educ:lunch_type 5 20.69 5857.6 1700.3
## + parent_educ:wkly_study_hours 10 115.36 5763.0 1700.7
## - parent_educ:practice_sport 10 289.90 6168.2 1700.8
## - ethnic_group:lunch_type 4 191.98 6070.3 1703.3
## - parent_marital_status:wkly_study_hours 5 217.55 6095.9 1703.8
## - ethnic_group:writing_score 4 219.33 6097.6 1706.0
## - ethnic_group:parent_educ 20 566.91 6445.2 1706.7
## - ethnic_group:parent_marital_status 10 466.20 6344.5 1717.4
##
## Step: AIC=1691.2
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:test_prep +
## lunch_type:parent_marital_status + lunch_type:wkly_study_hours +
## lunch_type:writing_score + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + test_prep:transport_means +
## parent_marital_status:is_first_child + parent_marital_status:wkly_study_hours +
## parent_marital_status:writing_score + practice_sport:is_first_child +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score +
## writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:test_prep 1 12.43 5899.2 1690.4
## - test_prep:transport_means 1 12.44 5899.2 1690.4
## - test_prep:practice_sport 2 39.61 5926.4 1691.2
## <none> 5886.7 1691.2
## - practice_sport:is_first_child 2 42.01 5928.8 1691.4
## - lunch_type:writing_score 1 22.57 5909.3 1691.5
## + is_first_child:math_score 1 16.22 5870.5 1691.6
## - writing_score:math_score 1 25.55 5912.3 1691.8
## - gender:writing_score 1 28.30 5915.0 1692.0
## - gender:math_score 1 29.44 5916.2 1692.1
## + parent_educ:is_first_child 5 88.77 5798.0 1692.2
## + is_first_child:writing_score 1 8.43 5878.3 1692.3
## - parent_marital_status:is_first_child 2 51.92 5938.7 1692.4
## + lunch_type:practice_sport 2 27.40 5859.3 1692.5
## + test_prep:writing_score 1 6.10 5880.6 1692.6
## + test_prep:wkly_study_hours 2 25.61 5861.1 1692.6
## + gender:is_first_child 1 5.42 5881.3 1692.7
## + test_prep:math_score 1 5.41 5881.3 1692.7
## + transport_means:math_score 1 5.41 5881.3 1692.7
## + gender:lunch_type 1 3.53 5883.2 1692.8
## - gender:parent_educ 5 117.57 6004.3 1692.9
## + gender:transport_means 1 2.78 5884.0 1692.9
## + transport_means:wkly_study_hours 2 22.50 5864.2 1692.9
## + lunch_type:is_first_child 1 1.98 5884.8 1693.0
## + gender:test_prep 1 1.19 5885.6 1693.1
## - wkly_study_hours:math_score 2 59.06 5945.8 1693.1
## + lunch_type:transport_means 1 1.02 5885.7 1693.1
## + lunch_type:math_score 1 0.28 5886.5 1693.2
## - test_prep:parent_marital_status 2 61.18 5947.9 1693.3
## - ethnic_group:transport_means 4 103.66 5990.4 1693.5
## + gender:parent_marital_status 3 35.77 5851.0 1693.6
## - lunch_type:wkly_study_hours 2 64.37 5951.1 1693.6
## - gender:practice_sport 2 64.76 5951.5 1693.7
## - parent_marital_status:writing_score 3 85.46 5972.2 1693.7
## - test_prep:is_first_child 1 45.80 5932.5 1693.8
## - lunch_type:parent_marital_status 3 86.41 5973.2 1693.8
## - practice_sport:writing_score 2 66.46 5953.2 1693.8
## + is_first_child:wkly_study_hours 2 12.15 5874.6 1694.0
## - ethnic_group:practice_sport 8 190.92 6077.7 1694.0
## - wkly_study_hours:writing_score 2 69.90 5956.6 1694.2
## + ethnic_group:test_prep 4 48.66 5838.1 1694.3
## + practice_sport:transport_means 2 7.87 5878.9 1694.4
## - parent_educ:test_prep 5 133.98 6020.7 1694.5
## - gender:wkly_study_hours 2 77.47 5964.2 1694.9
## + parent_marital_status:transport_means 3 22.08 5864.7 1695.0
## + parent_marital_status:practice_sport 4 41.77 5845.0 1695.0
## - ethnic_group:wkly_study_hours 8 201.56 6088.3 1695.1
## - is_first_child:transport_means 1 59.23 5946.0 1695.1
## + practice_sport:wkly_study_hours 4 40.45 5846.3 1695.1
## + parent_educ:transport_means 5 58.77 5828.0 1695.3
## - parent_educ:math_score 5 147.79 6034.5 1695.8
## + parent_marital_status:math_score 3 11.83 5874.9 1696.0
## + parent_educ:writing_score 5 45.41 5841.3 1696.6
## - parent_educ:parent_marital_status 14 347.41 6234.2 1697.0
## - transport_means:writing_score 1 81.02 5967.8 1697.3
## - practice_sport:math_score 2 102.76 5989.5 1697.4
## + ethnic_group:is_first_child 4 10.04 5876.7 1698.2
## + gender:ethnic_group 4 5.97 5880.8 1698.6
## + ethnic_group:math_score 4 1.90 5884.8 1699.0
## + parent_educ:lunch_type 5 19.46 5867.3 1699.2
## - parent_educ:practice_sport 10 290.44 6177.2 1699.6
## + parent_educ:wkly_study_hours 10 114.38 5772.4 1699.6
## - ethnic_group:lunch_type 4 189.41 6076.2 1701.9
## - parent_marital_status:wkly_study_hours 5 214.11 6100.9 1702.3
## - ethnic_group:writing_score 4 215.39 6102.1 1704.4
## - ethnic_group:parent_educ 20 561.52 6448.3 1705.0
## - ethnic_group:parent_marital_status 10 463.57 6350.3 1715.9
##
## Step: AIC=1690.44
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + test_prep:transport_means + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - test_prep:transport_means 1 12.25 5911.4 1689.7
## - lunch_type:writing_score 1 15.93 5915.1 1690.0
## - test_prep:practice_sport 2 37.78 5937.0 1690.2
## <none> 5899.2 1690.4
## - practice_sport:is_first_child 2 42.62 5941.8 1690.7
## + is_first_child:math_score 1 15.92 5883.3 1690.8
## - writing_score:math_score 1 24.73 5923.9 1690.9
## - gender:writing_score 1 27.35 5926.5 1691.2
## + lunch_type:test_prep 1 12.43 5886.7 1691.2
## + parent_educ:is_first_child 5 89.27 5809.9 1691.5
## - gender:math_score 1 30.28 5929.5 1691.5
## + lunch_type:practice_sport 2 29.56 5869.6 1691.5
## + test_prep:wkly_study_hours 2 29.14 5870.0 1691.5
## + is_first_child:writing_score 1 8.28 5890.9 1691.6
## - parent_marital_status:is_first_child 2 51.96 5951.1 1691.6
## + transport_means:math_score 1 5.83 5893.3 1691.9
## + gender:is_first_child 1 4.54 5894.6 1692.0
## + lunch_type:is_first_child 1 2.50 5896.7 1692.2
## + gender:transport_means 1 2.48 5896.7 1692.2
## - gender:parent_educ 5 118.69 6017.9 1692.2
## - wkly_study_hours:math_score 2 58.06 5957.2 1692.2
## + gender:lunch_type 1 1.97 5897.2 1692.2
## + lunch_type:transport_means 1 1.92 5897.3 1692.2
## + test_prep:writing_score 1 1.71 5897.5 1692.3
## + gender:test_prep 1 1.50 5897.7 1692.3
## + test_prep:math_score 1 0.58 5898.6 1692.4
## + lunch_type:math_score 1 0.06 5899.1 1692.4
## + gender:parent_marital_status 3 39.32 5859.9 1692.5
## + transport_means:wkly_study_hours 2 19.04 5880.1 1692.5
## - ethnic_group:transport_means 4 103.75 6002.9 1692.7
## - test_prep:parent_marital_status 2 65.17 5964.3 1692.9
## - test_prep:is_first_child 1 45.35 5944.5 1693.0
## - lunch_type:wkly_study_hours 2 66.00 5965.2 1693.0
## - ethnic_group:practice_sport 8 189.85 6089.0 1693.1
## - wkly_study_hours:writing_score 2 69.72 5968.9 1693.4
## - practice_sport:writing_score 2 69.75 5968.9 1693.4
## + is_first_child:wkly_study_hours 2 10.58 5888.6 1693.4
## - parent_marital_status:writing_score 3 90.40 5989.6 1693.4
## + practice_sport:transport_means 2 9.55 5889.6 1693.5
## - lunch_type:parent_marital_status 3 91.23 5990.4 1693.5
## + ethnic_group:test_prep 4 49.00 5850.2 1693.5
## - gender:practice_sport 2 71.32 5970.5 1693.5
## - is_first_child:transport_means 1 55.64 5954.8 1694.0
## - gender:wkly_study_hours 2 77.53 5976.7 1694.2
## + parent_marital_status:practice_sport 4 42.71 5856.5 1694.2
## + parent_marital_status:transport_means 3 22.10 5877.1 1694.2
## - parent_educ:test_prep 5 141.35 6040.5 1694.4
## + parent_educ:transport_means 5 58.31 5840.9 1694.6
## + practice_sport:wkly_study_hours 4 34.72 5864.5 1695.0
## + parent_marital_status:math_score 3 14.14 5885.0 1695.0
## - parent_educ:math_score 5 150.70 6049.9 1695.3
## - parent_educ:parent_marital_status 14 339.49 6238.7 1695.5
## - ethnic_group:wkly_study_hours 8 214.12 6113.3 1695.5
## + parent_educ:writing_score 5 46.77 5852.4 1695.8
## - transport_means:writing_score 1 83.01 5982.2 1696.7
## - practice_sport:math_score 2 106.94 6006.1 1697.0
## + ethnic_group:is_first_child 4 11.60 5887.6 1697.3
## + gender:ethnic_group 4 5.72 5893.5 1697.9
## + parent_educ:lunch_type 5 22.71 5876.5 1698.2
## + ethnic_group:math_score 4 2.06 5897.1 1698.2
## - parent_educ:practice_sport 10 288.27 6187.4 1698.6
## + parent_educ:wkly_study_hours 10 109.01 5790.2 1699.4
## - ethnic_group:lunch_type 4 182.54 6081.7 1700.4
## - parent_marital_status:wkly_study_hours 5 207.87 6107.0 1700.9
## - ethnic_group:writing_score 4 212.67 6111.8 1703.3
## - ethnic_group:parent_educ 20 560.24 6459.4 1704.0
## - ethnic_group:parent_marital_status 10 484.31 6383.5 1717.0
##
## Step: AIC=1689.67
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + lunch_type:writing_score +
## test_prep:parent_marital_status + test_prep:practice_sport +
## test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - lunch_type:writing_score 1 15.55 5927.0 1689.2
## - test_prep:practice_sport 2 37.89 5949.3 1689.4
## <none> 5911.4 1689.7
## - practice_sport:is_first_child 2 42.53 5954.0 1689.9
## - writing_score:math_score 1 24.01 5935.4 1690.1
## - gender:writing_score 1 25.56 5937.0 1690.2
## + is_first_child:math_score 1 14.41 5897.0 1690.2
## + test_prep:transport_means 1 12.25 5899.2 1690.4
## + lunch_type:test_prep 1 12.24 5899.2 1690.4
## - gender:math_score 1 30.06 5941.5 1690.7
## + test_prep:wkly_study_hours 2 29.98 5881.4 1690.7
## - parent_marital_status:is_first_child 2 51.50 5962.9 1690.8
## + lunch_type:practice_sport 2 28.06 5883.4 1690.9
## + parent_educ:is_first_child 5 86.91 5824.5 1690.9
## + transport_means:math_score 1 7.35 5904.1 1690.9
## + is_first_child:writing_score 1 7.18 5904.2 1691.0
## - ethnic_group:transport_means 4 95.91 6007.3 1691.2
## + gender:is_first_child 1 4.96 5906.5 1691.2
## + lunch_type:transport_means 1 3.41 5908.0 1691.3
## + lunch_type:is_first_child 1 1.70 5909.7 1691.5
## + gender:lunch_type 1 1.51 5909.9 1691.5
## + test_prep:writing_score 1 1.29 5910.1 1691.5
## - wkly_study_hours:math_score 2 59.29 5970.7 1691.5
## + gender:test_prep 1 0.95 5910.5 1691.6
## + gender:transport_means 1 0.86 5910.6 1691.6
## + test_prep:math_score 1 0.39 5911.0 1691.6
## + lunch_type:math_score 1 0.09 5911.3 1691.7
## - test_prep:parent_marital_status 2 60.68 5972.1 1691.7
## + gender:parent_marital_status 3 39.33 5872.1 1691.7
## + transport_means:wkly_study_hours 2 18.95 5892.5 1691.8
## - gender:parent_educ 5 124.02 6035.4 1691.9
## - test_prep:is_first_child 1 43.58 5955.0 1692.0
## - ethnic_group:practice_sport 8 189.86 6101.3 1692.3
## + ethnic_group:test_prep 4 53.26 5858.2 1692.3
## - practice_sport:writing_score 2 67.87 5979.3 1692.4
## - parent_marital_status:writing_score 3 88.30 5999.7 1692.4
## - gender:practice_sport 2 68.65 5980.1 1692.5
## - lunch_type:parent_marital_status 3 89.57 6001.0 1692.5
## + is_first_child:wkly_study_hours 2 10.41 5901.0 1692.6
## - wkly_study_hours:writing_score 2 72.31 5983.7 1692.8
## + practice_sport:transport_means 2 7.75 5903.7 1692.9
## - lunch_type:wkly_study_hours 2 73.89 5985.3 1693.0
## + parent_marital_status:practice_sport 4 43.58 5867.8 1693.3
## - gender:wkly_study_hours 2 78.42 5989.8 1693.4
## - is_first_child:transport_means 1 58.71 5970.1 1693.5
## - parent_educ:test_prep 5 143.50 6054.9 1693.8
## + parent_marital_status:transport_means 3 18.25 5893.2 1693.8
## - ethnic_group:wkly_study_hours 8 207.30 6118.7 1694.0
## + parent_educ:transport_means 5 56.18 5855.2 1694.0
## + parent_marital_status:math_score 3 15.33 5896.1 1694.1
## + practice_sport:wkly_study_hours 4 32.20 5879.2 1694.4
## - parent_educ:parent_marital_status 14 338.06 6249.5 1694.5
## - parent_educ:math_score 5 152.83 6064.3 1694.7
## - transport_means:writing_score 1 71.87 5983.3 1694.8
## + parent_educ:writing_score 5 44.22 5867.2 1695.2
## - practice_sport:math_score 2 105.16 6016.6 1696.1
## + ethnic_group:is_first_child 4 12.91 5898.5 1696.4
## + gender:ethnic_group 4 5.97 5905.5 1697.1
## - parent_educ:practice_sport 10 281.22 6192.6 1697.1
## + parent_educ:lunch_type 5 24.49 5886.9 1697.2
## + ethnic_group:math_score 4 1.82 5909.6 1697.5
## + parent_educ:wkly_study_hours 10 112.19 5799.2 1698.4
## - ethnic_group:lunch_type 4 176.49 6087.9 1699.0
## - parent_marital_status:wkly_study_hours 5 209.71 6121.1 1700.2
## - ethnic_group:writing_score 4 206.40 6117.8 1701.9
## - ethnic_group:parent_educ 20 550.34 6461.8 1702.2
## - ethnic_group:parent_marital_status 10 489.04 6400.5 1716.6
##
## Step: AIC=1689.22
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score + writing_score:math_score
##
## Df Sum of Sq RSS AIC
## - writing_score:math_score 1 11.36 5938.3 1688.3
## - test_prep:practice_sport 2 36.79 5963.8 1688.9
## <none> 5927.0 1689.2
## - practice_sport:is_first_child 2 42.54 5969.5 1689.4
## + lunch_type:writing_score 1 15.55 5911.4 1689.7
## + is_first_child:math_score 1 15.07 5911.9 1689.7
## + test_prep:wkly_study_hours 2 32.14 5894.8 1690.0
## - gender:writing_score 1 28.29 5955.3 1690.0
## + test_prep:transport_means 1 11.87 5915.1 1690.0
## + is_first_child:writing_score 1 8.52 5918.5 1690.4
## + lunch_type:practice_sport 2 27.32 5899.7 1690.5
## + transport_means:math_score 1 7.03 5919.9 1690.5
## + lunch_type:math_score 1 6.95 5920.0 1690.5
## + parent_educ:is_first_child 5 86.50 5840.5 1690.5
## + lunch_type:test_prep 1 5.72 5921.3 1690.7
## - gender:math_score 1 34.80 5961.8 1690.7
## + gender:is_first_child 1 4.59 5922.4 1690.8
## - parent_marital_status:is_first_child 2 56.16 5983.1 1690.8
## + lunch_type:transport_means 1 3.48 5923.5 1690.9
## - gender:parent_educ 5 119.47 6046.5 1691.0
## + lunch_type:is_first_child 1 1.41 5925.6 1691.1
## + gender:transport_means 1 0.76 5926.2 1691.1
## + gender:test_prep 1 0.73 5926.3 1691.1
## + transport_means:wkly_study_hours 2 20.66 5906.3 1691.2
## + test_prep:writing_score 1 0.36 5926.6 1691.2
## + gender:lunch_type 1 0.19 5926.8 1691.2
## + test_prep:math_score 1 0.06 5926.9 1691.2
## + gender:parent_marital_status 3 39.57 5887.4 1691.3
## + ethnic_group:test_prep 4 58.10 5868.9 1691.4
## - ethnic_group:transport_means 4 103.61 6030.6 1691.4
## - test_prep:parent_marital_status 2 63.41 5990.4 1691.5
## - test_prep:is_first_child 1 43.27 5970.2 1691.5
## - wkly_study_hours:math_score 2 65.79 5992.8 1691.7
## + is_first_child:wkly_study_hours 2 10.49 5916.5 1692.2
## - gender:practice_sport 2 71.09 5998.1 1692.2
## - practice_sport:writing_score 2 71.50 5998.5 1692.3
## - ethnic_group:practice_sport 8 195.15 6122.1 1692.3
## + parent_marital_status:practice_sport 4 48.88 5878.1 1692.3
## - lunch_type:parent_marital_status 3 93.82 6020.8 1692.5
## + practice_sport:transport_means 2 7.16 5919.8 1692.5
## - wkly_study_hours:writing_score 2 74.64 6001.6 1692.6
## - ethnic_group:wkly_study_hours 8 200.15 6127.1 1692.8
## - lunch_type:wkly_study_hours 2 78.06 6005.0 1692.9
## - gender:wkly_study_hours 2 79.96 6006.9 1693.1
## - parent_educ:test_prep 5 142.47 6069.5 1693.2
## - parent_marital_status:writing_score 3 101.61 6028.6 1693.2
## + parent_marital_status:transport_means 3 19.41 5907.6 1693.3
## - is_first_child:transport_means 1 62.87 5989.8 1693.4
## + parent_marital_status:math_score 3 16.76 5910.2 1693.5
## + parent_educ:transport_means 5 54.19 5872.8 1693.8
## + practice_sport:wkly_study_hours 4 33.36 5893.6 1693.9
## - parent_educ:parent_marital_status 14 340.95 6267.9 1694.2
## - parent_educ:math_score 5 153.92 6080.9 1694.3
## - transport_means:writing_score 1 73.63 6000.6 1694.5
## + parent_educ:writing_score 5 37.49 5889.5 1695.5
## - practice_sport:math_score 2 108.51 6035.5 1695.9
## + ethnic_group:is_first_child 4 12.94 5914.0 1695.9
## + parent_educ:lunch_type 5 26.51 5900.5 1696.6
## - parent_educ:practice_sport 10 281.57 6208.5 1696.6
## + gender:ethnic_group 4 5.15 5921.8 1696.7
## + ethnic_group:math_score 4 2.74 5924.2 1696.9
## - ethnic_group:lunch_type 4 171.72 6098.7 1698.1
## + parent_educ:wkly_study_hours 10 105.62 5821.4 1698.6
## - parent_marital_status:wkly_study_hours 5 214.43 6141.4 1700.2
## - ethnic_group:parent_educ 20 542.46 6469.4 1700.9
## - ethnic_group:writing_score 4 212.08 6139.1 1702.0
## - ethnic_group:parent_marital_status 10 480.12 6407.1 1715.2
##
## Step: AIC=1688.35
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:practice_sport + test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score
##
## Df Sum of Sq RSS AIC
## - test_prep:practice_sport 2 34.25 5972.6 1687.7
## <none> 5938.3 1688.3
## - practice_sport:is_first_child 2 42.31 5980.6 1688.5
## + is_first_child:math_score 1 18.12 5920.2 1688.5
## - gender:writing_score 1 24.36 5962.7 1688.8
## + test_prep:wkly_study_hours 2 32.33 5906.0 1689.1
## + test_prep:transport_means 1 11.48 5926.9 1689.2
## + writing_score:math_score 1 11.36 5927.0 1689.2
## + is_first_child:writing_score 1 10.84 5927.5 1689.3
## - gender:math_score 1 30.76 5969.1 1689.4
## + lunch_type:test_prep 1 7.73 5930.6 1689.6
## + lunch_type:practice_sport 2 26.76 5911.6 1689.7
## - parent_marital_status:is_first_child 2 54.56 5992.9 1689.7
## + transport_means:math_score 1 5.96 5932.4 1689.8
## + gender:is_first_child 1 4.27 5934.1 1689.9
## + gender:parent_marital_status 3 43.73 5894.6 1690.0
## + parent_educ:is_first_child 5 83.40 5854.9 1690.0
## + lunch_type:transport_means 1 3.17 5935.2 1690.0
## + lunch_type:writing_score 1 2.91 5935.4 1690.1
## + lunch_type:is_first_child 1 1.34 5937.0 1690.2
## + test_prep:math_score 1 0.92 5937.4 1690.3
## + gender:test_prep 1 0.91 5937.4 1690.3
## + gender:transport_means 1 0.58 5937.8 1690.3
## + test_prep:writing_score 1 0.21 5938.1 1690.3
## + gender:lunch_type 1 0.17 5938.2 1690.3
## - test_prep:parent_marital_status 2 60.55 5998.9 1690.3
## + lunch_type:math_score 1 0.11 5938.2 1690.3
## + transport_means:wkly_study_hours 2 19.86 5918.5 1690.4
## - test_prep:is_first_child 1 42.31 5980.7 1690.5
## - gender:parent_educ 5 124.51 6062.9 1690.6
## + ethnic_group:test_prep 4 54.32 5884.0 1690.9
## - ethnic_group:transport_means 4 110.04 6048.4 1691.2
## + parent_marital_status:practice_sport 4 49.69 5888.6 1691.4
## - ethnic_group:practice_sport 8 195.12 6133.5 1691.4
## + is_first_child:wkly_study_hours 2 9.14 5929.2 1691.4
## - wkly_study_hours:math_score 2 72.30 6010.6 1691.5
## - practice_sport:writing_score 2 72.58 6010.9 1691.5
## + practice_sport:transport_means 2 7.87 5930.5 1691.6
## - gender:practice_sport 2 73.60 6011.9 1691.6
## - lunch_type:parent_marital_status 3 94.38 6032.7 1691.7
## - wkly_study_hours:writing_score 2 80.34 6018.7 1692.3
## + parent_marital_status:transport_means 3 20.49 5917.9 1692.3
## - lunch_type:wkly_study_hours 2 81.57 6019.9 1692.4
## + parent_marital_status:math_score 3 18.57 5919.8 1692.5
## - gender:wkly_study_hours 2 82.69 6021.0 1692.5
## - parent_educ:math_score 5 145.08 6083.4 1692.6
## - parent_educ:test_prep 5 145.37 6083.7 1692.6
## - is_first_child:transport_means 1 64.92 6003.3 1692.8
## - parent_marital_status:writing_score 3 106.48 6044.8 1692.8
## - ethnic_group:wkly_study_hours 8 209.94 6148.3 1692.8
## + parent_educ:transport_means 5 53.99 5884.4 1693.0
## + practice_sport:wkly_study_hours 4 31.07 5907.3 1693.2
## - parent_educ:parent_marital_status 14 347.81 6286.2 1693.9
## - transport_means:writing_score 1 78.56 6016.9 1694.1
## + parent_educ:writing_score 5 37.06 5901.3 1694.7
## + ethnic_group:is_first_child 4 14.02 5924.3 1695.0
## - practice_sport:math_score 2 112.57 6050.9 1695.4
## + parent_educ:lunch_type 5 26.91 5911.4 1695.7
## + gender:ethnic_group 4 5.71 5932.6 1695.8
## - parent_educ:practice_sport 10 283.33 6221.7 1695.8
## + ethnic_group:math_score 4 3.77 5934.6 1696.0
## - ethnic_group:lunch_type 4 169.69 6108.0 1697.0
## + parent_educ:wkly_study_hours 10 101.61 5836.7 1698.2
## - parent_marital_status:wkly_study_hours 5 212.14 6150.5 1699.1
## - ethnic_group:parent_educ 20 544.84 6483.2 1700.1
## - ethnic_group:writing_score 4 225.95 6164.3 1702.4
## - ethnic_group:parent_marital_status 10 495.30 6433.6 1715.6
##
## Step: AIC=1687.74
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:is_first_child + practice_sport:writing_score +
## practice_sport:math_score + is_first_child:transport_means +
## transport_means:writing_score + wkly_study_hours:writing_score +
## wkly_study_hours:math_score
##
## Df Sum of Sq RSS AIC
## - practice_sport:is_first_child 2 38.50 6011.1 1687.5
## <none> 5972.6 1687.7
## + is_first_child:math_score 1 19.90 5952.7 1687.8
## - gender:writing_score 1 23.79 5996.4 1688.1
## + test_prep:practice_sport 2 34.25 5938.3 1688.3
## + is_first_child:writing_score 1 12.29 5960.3 1688.5
## + test_prep:transport_means 1 11.55 5961.0 1688.6
## + test_prep:wkly_study_hours 2 31.04 5941.5 1688.7
## + writing_score:math_score 1 8.82 5963.8 1688.9
## - gender:math_score 1 32.56 6005.2 1689.0
## + transport_means:math_score 1 7.26 5965.3 1689.0
## + lunch_type:test_prep 1 6.39 5966.2 1689.1
## + gender:is_first_child 1 4.37 5968.2 1689.3
## + parent_educ:is_first_child 5 84.19 5888.4 1689.4
## + lunch_type:transport_means 1 3.66 5968.9 1689.4
## + lunch_type:practice_sport 2 23.83 5948.8 1689.4
## + lunch_type:writing_score 1 3.27 5969.3 1689.4
## + gender:parent_marital_status 3 42.30 5930.3 1689.5
## - parent_marital_status:is_first_child 2 59.11 6031.7 1689.5
## + lunch_type:is_first_child 1 1.49 5971.1 1689.6
## + gender:test_prep 1 1.09 5971.5 1689.6
## + gender:transport_means 1 0.93 5971.7 1689.7
## + transport_means:wkly_study_hours 2 20.98 5951.6 1689.7
## + gender:lunch_type 1 0.32 5972.3 1689.7
## + lunch_type:math_score 1 0.25 5972.3 1689.7
## + test_prep:math_score 1 0.25 5972.3 1689.7
## + test_prep:writing_score 1 0.00 5972.6 1689.7
## - test_prep:is_first_child 1 41.65 6014.2 1689.8
## - test_prep:parent_marital_status 2 62.17 6034.8 1689.8
## - ethnic_group:practice_sport 8 187.15 6159.7 1689.9
## - gender:parent_educ 5 125.49 6098.1 1690.0
## + ethnic_group:test_prep 4 55.00 5917.6 1690.3
## - wkly_study_hours:math_score 2 70.21 6042.8 1690.6
## + is_first_child:wkly_study_hours 2 9.83 5962.8 1690.8
## + practice_sport:transport_means 2 9.29 5963.3 1690.8
## + parent_marital_status:practice_sport 4 47.82 5924.8 1691.0
## - lunch_type:wkly_study_hours 2 74.57 6047.2 1691.1
## - parent_educ:math_score 5 136.82 6109.4 1691.1
## - lunch_type:parent_marital_status 3 96.18 6068.8 1691.2
## - ethnic_group:transport_means 4 117.12 6089.7 1691.2
## - wkly_study_hours:writing_score 2 76.37 6049.0 1691.2
## - ethnic_group:wkly_study_hours 8 204.34 6176.9 1691.6
## + parent_marital_status:transport_means 3 21.55 5951.0 1691.6
## - practice_sport:writing_score 2 81.18 6053.8 1691.7
## - gender:wkly_study_hours 2 81.50 6054.1 1691.7
## + parent_marital_status:math_score 3 17.83 5954.8 1692.0
## - parent_marital_status:writing_score 3 106.86 6079.5 1692.2
## - gender:practice_sport 2 89.02 6061.6 1692.5
## - is_first_child:transport_means 1 68.79 6041.4 1692.5
## - parent_educ:test_prep 5 152.09 6124.7 1692.6
## + parent_educ:transport_means 5 51.34 5921.3 1692.7
## + practice_sport:wkly_study_hours 4 27.53 5945.1 1693.0
## - parent_educ:parent_marital_status 14 347.67 6320.3 1693.1
## - transport_means:writing_score 1 78.81 6051.4 1693.5
## + ethnic_group:is_first_child 4 13.31 5959.3 1694.4
## + parent_educ:writing_score 5 32.53 5940.1 1694.5
## + parent_educ:lunch_type 5 30.09 5942.5 1694.8
## + gender:ethnic_group 4 3.93 5968.7 1695.3
## - practice_sport:math_score 2 119.00 6091.6 1695.4
## + ethnic_group:math_score 4 3.40 5969.2 1695.4
## - ethnic_group:lunch_type 4 161.62 6134.2 1695.5
## - parent_marital_status:wkly_study_hours 5 201.35 6173.9 1697.3
## - ethnic_group:parent_educ 20 525.54 6498.1 1697.5
## - parent_educ:practice_sport 10 314.29 6286.9 1698.0
## + parent_educ:wkly_study_hours 10 96.65 5875.9 1698.1
## - ethnic_group:writing_score 4 214.40 6187.0 1700.5
## - ethnic_group:parent_marital_status 10 493.84 6466.4 1714.6
##
## Step: AIC=1687.53
## reading_score ~ gender + ethnic_group + parent_educ + lunch_type +
## test_prep + parent_marital_status + practice_sport + is_first_child +
## transport_means + wkly_study_hours + writing_score + math_score +
## gender:parent_educ + gender:practice_sport + gender:wkly_study_hours +
## gender:writing_score + gender:math_score + ethnic_group:parent_educ +
## ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score
##
## Df Sum of Sq RSS AIC
## <none> 6011.1 1687.5
## - gender:writing_score 1 21.37 6032.5 1687.6
## + is_first_child:math_score 1 19.32 5991.8 1687.6
## + practice_sport:is_first_child 2 38.50 5972.6 1687.7
## - parent_marital_status:is_first_child 2 47.96 6059.0 1688.2
## - gender:math_score 1 28.12 6039.2 1688.3
## + test_prep:transport_means 1 11.40 5999.7 1688.4
## - ethnic_group:practice_sport 8 175.00 6186.1 1688.5
## + test_prep:practice_sport 2 30.44 5980.6 1688.5
## + is_first_child:writing_score 1 10.10 6001.0 1688.5
## + test_prep:wkly_study_hours 2 29.45 5981.6 1688.6
## + writing_score:math_score 1 8.80 6002.3 1688.7
## - gender:parent_educ 5 114.74 6125.8 1688.7
## + transport_means:math_score 1 7.25 6003.8 1688.8
## + lunch_type:test_prep 1 7.15 6003.9 1688.8
## + gender:is_first_child 1 5.18 6005.9 1689.0
## + lunch_type:transport_means 1 4.83 6006.3 1689.1
## + lunch_type:writing_score 1 3.41 6007.7 1689.2
## + lunch_type:practice_sport 2 23.16 5987.9 1689.2
## + gender:lunch_type 1 1.33 6009.8 1689.4
## + transport_means:wkly_study_hours 2 21.47 5989.6 1689.4
## - test_prep:parent_marital_status 2 60.49 6071.6 1689.4
## + gender:transport_means 1 0.90 6010.2 1689.4
## + lunch_type:is_first_child 1 0.70 6010.4 1689.5
## + gender:test_prep 1 0.57 6010.5 1689.5
## + lunch_type:math_score 1 0.06 6011.0 1689.5
## + test_prep:math_score 1 0.03 6011.1 1689.5
## + test_prep:writing_score 1 0.02 6011.1 1689.5
## + parent_educ:is_first_child 5 80.68 5930.4 1689.6
## - parent_educ:math_score 5 123.96 6135.1 1689.6
## - test_prep:is_first_child 1 42.43 6053.5 1689.7
## + gender:parent_marital_status 3 38.29 5972.8 1689.8
## - ethnic_group:transport_means 4 107.80 6118.9 1690.0
## - wkly_study_hours:math_score 2 66.83 6077.9 1690.0
## - lunch_type:parent_marital_status 3 90.92 6102.0 1690.4
## + is_first_child:wkly_study_hours 2 10.72 6000.4 1690.5
## + parent_marital_status:practice_sport 4 50.08 5961.0 1690.6
## + ethnic_group:test_prep 4 46.62 5964.5 1690.9
## + practice_sport:transport_means 2 5.91 6005.2 1691.0
## - wkly_study_hours:writing_score 2 78.45 6089.5 1691.2
## - practice_sport:writing_score 2 78.56 6089.7 1691.2
## - lunch_type:wkly_study_hours 2 78.96 6090.1 1691.2
## - gender:practice_sport 2 84.25 6095.3 1691.7
## - ethnic_group:wkly_study_hours 8 210.31 6221.4 1691.8
## - gender:wkly_study_hours 2 85.43 6096.5 1691.9
## + parent_marital_status:math_score 3 16.97 5994.1 1691.9
## - parent_educ:test_prep 5 148.10 6159.2 1691.9
## - parent_marital_status:writing_score 3 107.18 6118.3 1692.0
## + parent_marital_status:transport_means 3 15.92 5995.2 1692.0
## - transport_means:writing_score 1 69.43 6080.5 1692.3
## - is_first_child:transport_means 1 69.60 6080.7 1692.3
## + parent_educ:transport_means 5 50.58 5960.5 1692.5
## + practice_sport:wkly_study_hours 4 25.75 5985.3 1693.0
## - parent_educ:parent_marital_status 14 351.47 6362.6 1693.1
## + parent_educ:writing_score 5 37.22 5973.9 1693.9
## + parent_educ:lunch_type 5 36.22 5974.9 1694.0
## + ethnic_group:is_first_child 4 14.25 5996.8 1694.1
## - practice_sport:math_score 2 113.60 6124.7 1694.6
## - ethnic_group:lunch_type 4 159.20 6170.3 1695.0
## + gender:ethnic_group 4 3.79 6007.3 1695.2
## + ethnic_group:math_score 4 3.63 6007.5 1695.2
## - parent_marital_status:wkly_study_hours 5 196.82 6207.9 1696.5
## - ethnic_group:parent_educ 20 528.60 6539.7 1697.3
## - parent_educ:practice_sport 10 313.80 6324.9 1697.5
## + parent_educ:wkly_study_hours 10 95.63 5915.5 1698.1
## - ethnic_group:writing_score 4 200.71 6211.8 1698.9
## - ethnic_group:parent_marital_status 10 481.20 6492.3 1713.0summary(stepwise_model_read2)##
## Call:
## lm(formula = reading_score ~ gender + ethnic_group + parent_educ +
## lunch_type + test_prep + parent_marital_status + practice_sport +
## is_first_child + transport_means + wkly_study_hours + writing_score +
## math_score + gender:parent_educ + gender:practice_sport +
## gender:wkly_study_hours + gender:writing_score + gender:math_score +
## ethnic_group:parent_educ + ethnic_group:lunch_type + ethnic_group:parent_marital_status +
## ethnic_group:practice_sport + ethnic_group:transport_means +
## ethnic_group:wkly_study_hours + ethnic_group:writing_score +
## parent_educ:test_prep + parent_educ:parent_marital_status +
## parent_educ:practice_sport + parent_educ:math_score + lunch_type:parent_marital_status +
## lunch_type:wkly_study_hours + test_prep:parent_marital_status +
## test_prep:is_first_child + parent_marital_status:is_first_child +
## parent_marital_status:wkly_study_hours + parent_marital_status:writing_score +
## practice_sport:writing_score + practice_sport:math_score +
## is_first_child:transport_means + transport_means:writing_score +
## wkly_study_hours:writing_score + wkly_study_hours:math_score,
## data = df_4_mdl_read2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0525 -2.1489 0.0223 2.2672 9.4698
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error
## (Intercept) -2.21476 6.05325
## gendermale -0.25828 2.69120
## ethnic_groupgroup B 4.79875 4.43458
## ethnic_groupgroup C 7.75833 4.17348
## ethnic_groupgroup D 5.28196 4.45744
## ethnic_groupgroup E -0.92056 4.68923
## parent_educbachelor's degree -1.34346 4.87623
## parent_educhigh school -4.03417 3.68396
## parent_educmaster's degree -13.00825 5.55005
## parent_educsome college 1.51613 3.74291
## parent_educsome high school -7.95960 3.43483
## lunch_typestandard -3.69403 1.79782
## test_prepnone -1.02047 1.41570
## parent_marital_statusmarried -6.94406 3.65991
## parent_marital_statussingle -9.79338 3.97973
## parent_marital_statuswidowed 28.09604 16.65583
## practice_sportregularly 4.30334 4.58906
## practice_sportsometimes 3.33813 4.49148
## is_first_childyes 0.30730 1.41663
## transport_meansschool_bus 1.47443 2.04096
## wkly_study_hours> 10 3.02830 3.69241
## wkly_study_hours10-May 4.27984 3.00443
## writing_score 0.93805 0.13802
## math_score 0.17400 0.12824
## gendermale:parent_educbachelor's degree 0.27908 1.31086
## gendermale:parent_educhigh school -1.37943 1.08076
## gendermale:parent_educmaster's degree -4.20026 1.84915
## gendermale:parent_educsome college -0.19030 1.09407
## gendermale:parent_educsome high school 0.33156 1.10834
## gendermale:practice_sportregularly 1.12615 2.02819
## gendermale:practice_sportsometimes 3.60461 1.95233
## gendermale:wkly_study_hours> 10 -4.31010 1.75256
## gendermale:wkly_study_hours10-May -1.35212 1.31064
## gendermale:writing_score -0.07647 0.06178
## gendermale:math_score 0.08058 0.05675
## ethnic_groupgroup B:parent_educbachelor's degree 1.80093 3.33610
## ethnic_groupgroup C:parent_educbachelor's degree 3.61920 3.26168
## ethnic_groupgroup D:parent_educbachelor's degree 3.01255 3.30049
## ethnic_groupgroup E:parent_educbachelor's degree 1.35304 3.71977
## ethnic_groupgroup B:parent_educhigh school 0.27504 2.13614
## ethnic_groupgroup C:parent_educhigh school 1.31485 2.02529
## ethnic_groupgroup D:parent_educhigh school 0.28283 2.11737
## ethnic_groupgroup E:parent_educhigh school 2.38191 2.35845
## ethnic_groupgroup B:parent_educmaster's degree 13.22752 4.04855
## ethnic_groupgroup C:parent_educmaster's degree 12.37096 3.84183
## ethnic_groupgroup D:parent_educmaster's degree 6.87697 3.74574
## ethnic_groupgroup E:parent_educmaster's degree 9.75762 4.16976
## ethnic_groupgroup B:parent_educsome college 0.64794 2.40932
## ethnic_groupgroup C:parent_educsome college 1.02442 2.24934
## ethnic_groupgroup D:parent_educsome college 1.15477 2.37057
## ethnic_groupgroup E:parent_educsome college 5.34836 2.43228
## ethnic_groupgroup B:parent_educsome high school 4.69093 2.23947
## ethnic_groupgroup C:parent_educsome high school 3.70174 2.18437
## ethnic_groupgroup D:parent_educsome high school 2.87097 2.19681
## ethnic_groupgroup E:parent_educsome high school 7.73872 2.39189
## ethnic_groupgroup B:lunch_typestandard 2.86667 1.58361
## ethnic_groupgroup C:lunch_typestandard 3.91173 1.52070
## ethnic_groupgroup D:lunch_typestandard 4.79843 1.54487
## ethnic_groupgroup E:lunch_typestandard 2.62414 1.70699
## ethnic_groupgroup B:parent_marital_statusmarried 7.40685 2.18629
## ethnic_groupgroup C:parent_marital_statusmarried 3.87793 2.10062
## ethnic_groupgroup D:parent_marital_statusmarried 2.25615 2.04995
## ethnic_groupgroup E:parent_marital_statusmarried 4.58007 2.26496
## ethnic_groupgroup B:parent_marital_statussingle 9.07991 2.54779
## ethnic_groupgroup C:parent_marital_statussingle 5.97661 2.44902
## ethnic_groupgroup D:parent_marital_statussingle 6.45149 2.41769
## ethnic_groupgroup E:parent_marital_statussingle 10.72172 2.71864
## ethnic_groupgroup B:parent_marital_statuswidowed -3.80756 18.56512
## ethnic_groupgroup C:parent_marital_statuswidowed 7.46402 30.50690
## ethnic_groupgroup D:parent_marital_statuswidowed -13.26686 14.72030
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly -3.83286 2.80925
## ethnic_groupgroup C:practice_sportregularly -5.49412 2.69971
## ethnic_groupgroup D:practice_sportregularly -4.87583 2.86891
## ethnic_groupgroup E:practice_sportregularly -0.94415 2.90183
## ethnic_groupgroup B:practice_sportsometimes -2.14747 2.95073
## ethnic_groupgroup C:practice_sportsometimes -3.63355 2.82067
## ethnic_groupgroup D:practice_sportsometimes -4.66182 3.00407
## ethnic_groupgroup E:practice_sportsometimes -0.92256 2.96174
## ethnic_groupgroup B:transport_meansschool_bus -0.42056 1.57754
## ethnic_groupgroup C:transport_meansschool_bus 0.60605 1.45416
## ethnic_groupgroup D:transport_meansschool_bus 2.38901 1.50959
## ethnic_groupgroup E:transport_meansschool_bus 1.62760 1.67793
## ethnic_groupgroup B:wkly_study_hours> 10 -1.89818 2.52835
## ethnic_groupgroup C:wkly_study_hours> 10 -1.51105 2.49342
## ethnic_groupgroup D:wkly_study_hours> 10 -4.02474 2.49719
## ethnic_groupgroup E:wkly_study_hours> 10 -2.66490 2.66132
## ethnic_groupgroup B:wkly_study_hours10-May -1.05320 2.17191
## ethnic_groupgroup C:wkly_study_hours10-May -2.75061 2.14577
## ethnic_groupgroup D:wkly_study_hours10-May -3.83976 2.18461
## ethnic_groupgroup E:wkly_study_hours10-May -5.25480 2.37169
## ethnic_groupgroup B:writing_score -0.16442 0.04847
## ethnic_groupgroup C:writing_score -0.16444 0.04776
## ethnic_groupgroup D:writing_score -0.12672 0.04778
## ethnic_groupgroup E:writing_score -0.10342 0.05396
## parent_educbachelor's degree:test_prepnone -1.00503 1.27661
## parent_educhigh school:test_prepnone 1.01928 1.16640
## parent_educmaster's degree:test_prepnone 4.60672 1.96432
## parent_educsome college:test_prepnone -1.17611 1.15786
## parent_educsome high school:test_prepnone 0.35747 1.10318
## parent_educbachelor's degree:parent_marital_statusmarried -2.18740 2.33245
## parent_educhigh school:parent_marital_statusmarried 1.80301 1.65539
## parent_educmaster's degree:parent_marital_statusmarried -6.30035 2.35025
## parent_educsome college:parent_marital_statusmarried -1.88890 1.58412
## parent_educsome high school:parent_marital_statusmarried -0.76985 1.56287
## parent_educbachelor's degree:parent_marital_statussingle -0.87797 2.65282
## parent_educhigh school:parent_marital_statussingle 1.27707 1.82206
## parent_educmaster's degree:parent_marital_statussingle -2.48327 2.42624
## parent_educsome college:parent_marital_statussingle -1.12806 1.78648
## parent_educsome high school:parent_marital_statussingle 1.75508 1.74397
## parent_educbachelor's degree:parent_marital_statuswidowed 13.67748 13.51473
## parent_educhigh school:parent_marital_statuswidowed -16.26360 16.73436
## parent_educmaster's degree:parent_marital_statuswidowed -14.68575 15.60756
## parent_educsome college:parent_marital_statuswidowed 6.06937 19.94302
## parent_educsome high school:parent_marital_statuswidowed -0.90945 11.16785
## parent_educbachelor's degree:practice_sportregularly -3.83925 2.38818
## parent_educhigh school:practice_sportregularly -1.53783 1.97962
## parent_educmaster's degree:practice_sportregularly 0.02556 2.73642
## parent_educsome college:practice_sportregularly 1.60463 2.03344
## parent_educsome high school:practice_sportregularly -0.36100 1.88111
## parent_educbachelor's degree:practice_sportsometimes -3.59853 2.33333
## parent_educhigh school:practice_sportsometimes -0.60209 1.90898
## parent_educmaster's degree:practice_sportsometimes -1.52626 2.50252
## parent_educsome college:practice_sportsometimes 0.48721 1.97873
## parent_educsome high school:practice_sportsometimes 3.04852 1.80284
## parent_educbachelor's degree:math_score 0.05130 0.04414
## parent_educhigh school:math_score 0.04416 0.03800
## parent_educmaster's degree:math_score 0.08309 0.06234
## parent_educsome college:math_score -0.03771 0.03788
## parent_educsome high school:math_score 0.05039 0.03615
## lunch_typestandard:parent_marital_statusmarried -0.92594 1.13379
## lunch_typestandard:parent_marital_statussingle 0.40177 1.31966
## lunch_typestandard:parent_marital_statuswidowed 15.42081 7.73865
## lunch_typestandard:wkly_study_hours> 10 1.52484 1.30358
## lunch_typestandard:wkly_study_hours10-May -1.09665 0.97682
## test_prepnone:parent_marital_statusmarried 2.40484 1.16596
## test_prepnone:parent_marital_statussingle 2.25693 1.31817
## test_prepnone:parent_marital_statuswidowed -15.88908 13.47017
## test_prepnone:is_first_childyes 1.39949 0.80241
## parent_marital_statusmarried:is_first_childyes -2.23441 1.27424
## parent_marital_statussingle:is_first_childyes -1.37971 1.40260
## parent_marital_statuswidowed:is_first_childyes 16.48409 11.02305
## parent_marital_statusmarried:wkly_study_hours> 10 2.85843 1.75319
## parent_marital_statussingle:wkly_study_hours> 10 4.02397 1.93428
## parent_marital_statuswidowed:wkly_study_hours> 10 10.22989 13.47410
## parent_marital_statusmarried:wkly_study_hours10-May -1.02820 1.23023
## parent_marital_statussingle:wkly_study_hours10-May -2.19040 1.37506
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 0.06963 0.04155
## parent_marital_statussingle:writing_score 0.04234 0.04633
## parent_marital_statuswidowed:writing_score -0.45567 0.24320
## practice_sportregularly:writing_score 0.16580 0.12044
## practice_sportsometimes:writing_score 0.25955 0.11670
## practice_sportregularly:math_score -0.20664 0.12037
## practice_sportsometimes:math_score -0.30668 0.11525
## is_first_childyes:transport_meansschool_bus 1.78661 0.79975
## transport_meansschool_bus:writing_score -0.05318 0.02383
## wkly_study_hours> 10:writing_score -0.21770 0.09572
## wkly_study_hours10-May:writing_score -0.11246 0.06877
## wkly_study_hours> 10:math_score 0.18527 0.09508
## wkly_study_hours10-May:math_score 0.13290 0.07180
## t value Pr(>|t|)
## (Intercept) -0.366 0.714635
## gendermale -0.096 0.923586
## ethnic_groupgroup B 1.082 0.279804
## ethnic_groupgroup C 1.859 0.063715 .
## ethnic_groupgroup D 1.185 0.236680
## ethnic_groupgroup E -0.196 0.844457
## parent_educbachelor's degree -0.276 0.783056
## parent_educhigh school -1.095 0.274101
## parent_educmaster's degree -2.344 0.019541 *
## parent_educsome college 0.405 0.685630
## parent_educsome high school -2.317 0.020954 *
## lunch_typestandard -2.055 0.040508 *
## test_prepnone -0.721 0.471406
## parent_marital_statusmarried -1.897 0.058453 .
## parent_marital_statussingle -2.461 0.014253 *
## parent_marital_statuswidowed 1.687 0.092354 .
## practice_sportregularly 0.938 0.348904
## practice_sportsometimes 0.743 0.457757
## is_first_childyes 0.217 0.828370
## transport_meansschool_bus 0.722 0.470429
## wkly_study_hours> 10 0.820 0.412589
## wkly_study_hours10-May 1.425 0.155023
## writing_score 6.796 3.58e-11 ***
## math_score 1.357 0.175554
## gendermale:parent_educbachelor's degree 0.213 0.831506
## gendermale:parent_educhigh school -1.276 0.202518
## gendermale:parent_educmaster's degree -2.271 0.023612 *
## gendermale:parent_educsome college -0.174 0.861998
## gendermale:parent_educsome high school 0.299 0.764972
## gendermale:practice_sportregularly 0.555 0.579014
## gendermale:practice_sportsometimes 1.846 0.065532 .
## gendermale:wkly_study_hours> 10 -2.459 0.014312 *
## gendermale:wkly_study_hours10-May -1.032 0.302813
## gendermale:writing_score -1.238 0.216467
## gendermale:math_score 1.420 0.156384
## ethnic_groupgroup B:parent_educbachelor's degree 0.540 0.589592
## ethnic_groupgroup C:parent_educbachelor's degree 1.110 0.267785
## ethnic_groupgroup D:parent_educbachelor's degree 0.913 0.361879
## ethnic_groupgroup E:parent_educbachelor's degree 0.364 0.716227
## ethnic_groupgroup B:parent_educhigh school 0.129 0.897611
## ethnic_groupgroup C:parent_educhigh school 0.649 0.516546
## ethnic_groupgroup D:parent_educhigh school 0.134 0.893800
## ethnic_groupgroup E:parent_educhigh school 1.010 0.313087
## ethnic_groupgroup B:parent_educmaster's degree 3.267 0.001173 **
## ethnic_groupgroup C:parent_educmaster's degree 3.220 0.001379 **
## ethnic_groupgroup D:parent_educmaster's degree 1.836 0.067055 .
## ethnic_groupgroup E:parent_educmaster's degree 2.340 0.019734 *
## ethnic_groupgroup B:parent_educsome college 0.269 0.788111
## ethnic_groupgroup C:parent_educsome college 0.455 0.649028
## ethnic_groupgroup D:parent_educsome college 0.487 0.626415
## ethnic_groupgroup E:parent_educsome college 2.199 0.028415 *
## ethnic_groupgroup B:parent_educsome high school 2.095 0.036784 *
## ethnic_groupgroup C:parent_educsome high school 1.695 0.090864 .
## ethnic_groupgroup D:parent_educsome high school 1.307 0.191949
## ethnic_groupgroup E:parent_educsome high school 3.235 0.001308 **
## ethnic_groupgroup B:lunch_typestandard 1.810 0.070959 .
## ethnic_groupgroup C:lunch_typestandard 2.572 0.010436 *
## ethnic_groupgroup D:lunch_typestandard 3.106 0.002021 **
## ethnic_groupgroup E:lunch_typestandard 1.537 0.124956
## ethnic_groupgroup B:parent_marital_statusmarried 3.388 0.000769 ***
## ethnic_groupgroup C:parent_marital_statusmarried 1.846 0.065565 .
## ethnic_groupgroup D:parent_marital_statusmarried 1.101 0.271690
## ethnic_groupgroup E:parent_marital_statusmarried 2.022 0.043779 *
## ethnic_groupgroup B:parent_marital_statussingle 3.564 0.000406 ***
## ethnic_groupgroup C:parent_marital_statussingle 2.440 0.015072 *
## ethnic_groupgroup D:parent_marital_statussingle 2.668 0.007908 **
## ethnic_groupgroup E:parent_marital_statussingle 3.944 9.36e-05 ***
## ethnic_groupgroup B:parent_marital_statuswidowed -0.205 0.837597
## ethnic_groupgroup C:parent_marital_statuswidowed 0.245 0.806831
## ethnic_groupgroup D:parent_marital_statuswidowed -0.901 0.367952
## ethnic_groupgroup E:parent_marital_statuswidowed NA NA
## ethnic_groupgroup B:practice_sportregularly -1.364 0.173163
## ethnic_groupgroup C:practice_sportregularly -2.035 0.042454 *
## ethnic_groupgroup D:practice_sportregularly -1.700 0.089938 .
## ethnic_groupgroup E:practice_sportregularly -0.325 0.745065
## ethnic_groupgroup B:practice_sportsometimes -0.728 0.467145
## ethnic_groupgroup C:practice_sportsometimes -1.288 0.198372
## ethnic_groupgroup D:practice_sportsometimes -1.552 0.121435
## ethnic_groupgroup E:practice_sportsometimes -0.311 0.755577
## ethnic_groupgroup B:transport_meansschool_bus -0.267 0.789910
## ethnic_groupgroup C:transport_meansschool_bus 0.417 0.677056
## ethnic_groupgroup D:transport_meansschool_bus 1.583 0.114256
## ethnic_groupgroup E:transport_meansschool_bus 0.970 0.332588
## ethnic_groupgroup B:wkly_study_hours> 10 -0.751 0.453209
## ethnic_groupgroup C:wkly_study_hours> 10 -0.606 0.544823
## ethnic_groupgroup D:wkly_study_hours> 10 -1.612 0.107758
## ethnic_groupgroup E:wkly_study_hours> 10 -1.001 0.317222
## ethnic_groupgroup B:wkly_study_hours10-May -0.485 0.627981
## ethnic_groupgroup C:wkly_study_hours10-May -1.282 0.200576
## ethnic_groupgroup D:wkly_study_hours10-May -1.758 0.079518 .
## ethnic_groupgroup E:wkly_study_hours10-May -2.216 0.027238 *
## ethnic_groupgroup B:writing_score -3.392 0.000758 ***
## ethnic_groupgroup C:writing_score -3.443 0.000632 ***
## ethnic_groupgroup D:writing_score -2.652 0.008299 **
## ethnic_groupgroup E:writing_score -1.917 0.055948 .
## parent_educbachelor's degree:test_prepnone -0.787 0.431560
## parent_educhigh school:test_prepnone 0.874 0.382675
## parent_educmaster's degree:test_prepnone 2.345 0.019470 *
## parent_educsome college:test_prepnone -1.016 0.310315
## parent_educsome high school:test_prepnone 0.324 0.746067
## parent_educbachelor's degree:parent_marital_statusmarried -0.938 0.348866
## parent_educhigh school:parent_marital_statusmarried 1.089 0.276685
## parent_educmaster's degree:parent_marital_statusmarried -2.681 0.007628 **
## parent_educsome college:parent_marital_statusmarried -1.192 0.233760
## parent_educsome high school:parent_marital_statusmarried -0.493 0.622556
## parent_educbachelor's degree:parent_marital_statussingle -0.331 0.740837
## parent_educhigh school:parent_marital_statussingle 0.701 0.483747
## parent_educmaster's degree:parent_marital_statussingle -1.024 0.306644
## parent_educsome college:parent_marital_statussingle -0.631 0.528086
## parent_educsome high school:parent_marital_statussingle 1.006 0.314802
## parent_educbachelor's degree:parent_marital_statuswidowed 1.012 0.312086
## parent_educhigh school:parent_marital_statuswidowed -0.972 0.331661
## parent_educmaster's degree:parent_marital_statuswidowed -0.941 0.347264
## parent_educsome college:parent_marital_statuswidowed 0.304 0.761019
## parent_educsome high school:parent_marital_statuswidowed -0.081 0.935134
## parent_educbachelor's degree:practice_sportregularly -1.608 0.108655
## parent_educhigh school:practice_sportregularly -0.777 0.437685
## parent_educmaster's degree:practice_sportregularly 0.009 0.992553
## parent_educsome college:practice_sportregularly 0.789 0.430474
## parent_educsome high school:practice_sportregularly -0.192 0.847906
## parent_educbachelor's degree:practice_sportsometimes -1.542 0.123752
## parent_educhigh school:practice_sportsometimes -0.315 0.752610
## parent_educmaster's degree:practice_sportsometimes -0.610 0.542257
## parent_educsome college:practice_sportsometimes 0.246 0.805627
## parent_educsome high school:practice_sportsometimes 1.691 0.091568 .
## parent_educbachelor's degree:math_score 1.162 0.245837
## parent_educhigh school:math_score 1.162 0.245750
## parent_educmaster's degree:math_score 1.333 0.183327
## parent_educsome college:math_score -0.995 0.320060
## parent_educsome high school:math_score 1.394 0.164075
## lunch_typestandard:parent_marital_statusmarried -0.817 0.414564
## lunch_typestandard:parent_marital_statussingle 0.304 0.760929
## lunch_typestandard:parent_marital_statuswidowed 1.993 0.046924 *
## lunch_typestandard:wkly_study_hours> 10 1.170 0.242756
## lunch_typestandard:wkly_study_hours10-May -1.123 0.262202
## test_prepnone:parent_marital_statusmarried 2.063 0.039755 *
## test_prepnone:parent_marital_statussingle 1.712 0.087585 .
## test_prepnone:parent_marital_statuswidowed -1.180 0.238820
## test_prepnone:is_first_childyes 1.744 0.081852 .
## parent_marital_statusmarried:is_first_childyes -1.754 0.080222 .
## parent_marital_statussingle:is_first_childyes -0.984 0.325824
## parent_marital_statuswidowed:is_first_childyes 1.495 0.135537
## parent_marital_statusmarried:wkly_study_hours> 10 1.630 0.103744
## parent_marital_statussingle:wkly_study_hours> 10 2.080 0.038084 *
## parent_marital_statuswidowed:wkly_study_hours> 10 0.759 0.448132
## parent_marital_statusmarried:wkly_study_hours10-May -0.836 0.403744
## parent_marital_statussingle:wkly_study_hours10-May -1.593 0.111906
## parent_marital_statuswidowed:wkly_study_hours10-May NA NA
## parent_marital_statusmarried:writing_score 1.676 0.094490 .
## parent_marital_statussingle:writing_score 0.914 0.361268
## parent_marital_statuswidowed:writing_score -1.874 0.061660 .
## practice_sportregularly:writing_score 1.377 0.169355
## practice_sportsometimes:writing_score 2.224 0.026653 *
## practice_sportregularly:math_score -1.717 0.086742 .
## practice_sportsometimes:math_score -2.661 0.008083 **
## is_first_childyes:transport_meansschool_bus 2.234 0.025997 *
## transport_meansschool_bus:writing_score -2.231 0.026183 *
## wkly_study_hours> 10:writing_score -2.274 0.023437 *
## wkly_study_hours10-May:writing_score -1.635 0.102739
## wkly_study_hours> 10:math_score 1.948 0.052008 .
## wkly_study_hours10-May:math_score 1.851 0.064862 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.735 on 431 degrees of freedom
## Multiple R-squared: 0.9555, Adjusted R-squared: 0.9392
## F-statistic: 58.6 on 158 and 431 DF, p-value: < 2.2e-16